CBSE Class 8

CBSE Class 8

RD Sharma Class 8 Solutions Chapter 3 Squares and Square Roots Ex 3.9

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RD Sharma Class 8 Solutions Chapter 3 Squares and Square Roots Ex 3.9

These Solutions are part of RD Sharma Class 8 Solutions. Here we have given RD Sharma Class 8 Solutions Chapter 3 Squares and Square Roots Ex 3.9

Other Exercises

Using square root table, find the square roots of the following :

Question 1.
7
Solution:
RD Sharma Class 8 Solutions Chapter 3 Squares and Square Roots Ex 3.9 1

Question 2.
15
Solution:
RD Sharma Class 8 Solutions Chapter 3 Squares and Square Roots Ex 3.9 2

Question 3.
74
Solution:
RD Sharma Class 8 Solutions Chapter 3 Squares and Square Roots Ex 3.9 3

Question 4.
82
Solution:
RD Sharma Class 8 Solutions Chapter 3 Squares and Square Roots Ex 3.9 4

Question 5.
198
Solution:
RD Sharma Class 8 Solutions Chapter 3 Squares and Square Roots Ex 3.9 5
RD Sharma Class 8 Solutions Chapter 3 Squares and Square Roots Ex 3.9 6

Question 6.
540
Solution:
RD Sharma Class 8 Solutions Chapter 3 Squares and Square Roots Ex 3.9 7

Question 7.
8700
Solution:
RD Sharma Class 8 Solutions Chapter 3 Squares and Square Roots Ex 3.9 8

Question 8.
3509
Solution:
RD Sharma Class 8 Solutions Chapter 3 Squares and Square Roots Ex 3.9 9
RD Sharma Class 8 Solutions Chapter 3 Squares and Square Roots Ex 3.9 10

Question 9.
6929
Solution:
RD Sharma Class 8 Solutions Chapter 3 Squares and Square Roots Ex 3.9 11

Question 10.
25725
Solution:
RD Sharma Class 8 Solutions Chapter 3 Squares and Square Roots Ex 3.9 12

Question 11.
1312
Solution:
RD Sharma Class 8 Solutions Chapter 3 Squares and Square Roots Ex 3.9 13

Question 12.
4192
Solution:
RD Sharma Class 8 Solutions Chapter 3 Squares and Square Roots Ex 3.9 14

Question 13.
4955
Solution:
RD Sharma Class 8 Solutions Chapter 3 Squares and Square Roots Ex 3.9 15

Question 14.
\(\frac {99 }{ 144 }\)
Solution:
RD Sharma Class 8 Solutions Chapter 3 Squares and Square Roots Ex 3.9 16

Question 15.
\(\frac {57 }{ 169 }\)
Solution:
RD Sharma Class 8 Solutions Chapter 3 Squares and Square Roots Ex 3.9 17

Question 16.
\(\frac {101 }{ 169 }\)
Solution:
RD Sharma Class 8 Solutions Chapter 3 Squares and Square Roots Ex 3.9 18

Question 17.
13.21
Solution:
RD Sharma Class 8 Solutions Chapter 3 Squares and Square Roots Ex 3.9 19
RD Sharma Class 8 Solutions Chapter 3 Squares and Square Roots Ex 3.9 20

Question 18.
21.97
Solution:
RD Sharma Class 8 Solutions Chapter 3 Squares and Square Roots Ex 3.9 21

Question 19.
110
Solution:
RD Sharma Class 8 Solutions Chapter 3 Squares and Square Roots Ex 3.9 22

Question 20.
1110
Solution:
RD Sharma Class 8 Solutions Chapter 3 Squares and Square Roots Ex 3.9 23

Question 21.
11.11
Solution:
RD Sharma Class 8 Solutions Chapter 3 Squares and Square Roots Ex 3.9 24

Question 22.
The area of a square field is 325 m2. Find the approximate length of one side of the field.
Solution:
RD Sharma Class 8 Solutions Chapter 3 Squares and Square Roots Ex 3.9 25

Question 23.
Find the length of a side of a square, whose area is equal to the area bf the rectangle with sides 240 m and 70 m.
Solution:
RD Sharma Class 8 Solutions Chapter 3 Squares and Square Roots Ex 3.9 26

Hope given RD Sharma Class 8 Solutions Chapter 3 Squares and Square Roots Ex 3.9 are helpful to complete your math homework.

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RD Sharma Class 8 Solutions Chapter 3 Squares and Square Roots Ex 3.8

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RD Sharma Class 8 Solutions Chapter 3 Squares and Square Roots Ex 3.8

These Solutions are part of RD Sharma Class 8 Solutions. Here we have given RD Sharma Class 8 Solutions Chapter 3 Squares and Square Roots Ex 3.8

Other Exercises

Question 1.
Find the square root of each of the following correct to three places of decimal :
(i) 5
(ii) 7
(iii) 17
(iv) 20
(v) 66
(vi) 427
(vii) 1.7
(vii’) 23.1
(ix) 2.5
(x) 237.615
(xi) 15.3215
(xii) 0.9
(xiii) 0.1
(xiv) 0.016
(xv) 0.00064
(xvi) 0.019
(xvii) \(\frac {7 }{ 8 }\)
(xviii) \(\frac {5 }{ 12 }\)
(xix) 2 \(\frac {1 }{ 2 }\)
(xx) 287 \(\frac {8 }{ 8 }\)
Solution:
RD Sharma Class 8 Solutions Chapter 3 Squares and Square Roots Ex 3.8 1
RD Sharma Class 8 Solutions Chapter 3 Squares and Square Roots Ex 3.8 2
RD Sharma Class 8 Solutions Chapter 3 Squares and Square Roots Ex 3.8 3
RD Sharma Class 8 Solutions Chapter 3 Squares and Square Roots Ex 3.8 4
RD Sharma Class 8 Solutions Chapter 3 Squares and Square Roots Ex 3.8 5
RD Sharma Class 8 Solutions Chapter 3 Squares and Square Roots Ex 3.8 6
RD Sharma Class 8 Solutions Chapter 3 Squares and Square Roots Ex 3.8 7
RD Sharma Class 8 Solutions Chapter 3 Squares and Square Roots Ex 3.8 8
RD Sharma Class 8 Solutions Chapter 3 Squares and Square Roots Ex 3.8 9
RD Sharma Class 8 Solutions Chapter 3 Squares and Square Roots Ex 3.8 10
RD Sharma Class 8 Solutions Chapter 3 Squares and Square Roots Ex 3.8 11

Question 2.
Find the square root of 12.0068 correct to four decimal places.
Solution:
RD Sharma Class 8 Solutions Chapter 3 Squares and Square Roots Ex 3.8 12

Question 3.
Find the square root of 11 correct to five decimal places.
Solution:
RD Sharma Class 8 Solutions Chapter 3 Squares and Square Roots Ex 3.8 13

Question 4.
Given that √2, = 1-414, √3 = 1.732, √5 = 2.236 and √7 = 2.646. Evaluate each of the following :
RD Sharma Class 8 Solutions Chapter 3 Squares and Square Roots Ex 3.8 14
Solution:
RD Sharma Class 8 Solutions Chapter 3 Squares and Square Roots Ex 3.8 15
RD Sharma Class 8 Solutions Chapter 3 Squares and Square Roots Ex 3.8 16

Question 5.
Given that √2 = 1-414, √3 = 1-732, √5= 2.236 and √7= 2.646, find the square roots of the following :
RD Sharma Class 8 Solutions Chapter 3 Squares and Square Roots Ex 3.8 17
Solution:
RD Sharma Class 8 Solutions Chapter 3 Squares and Square Roots Ex 3.8 18
RD Sharma Class 8 Solutions Chapter 3 Squares and Square Roots Ex 3.8 19
RD Sharma Class 8 Solutions Chapter 3 Squares and Square Roots Ex 3.8 20

Hope given RD Sharma Class 8 Solutions Chapter 3 Squares and Square Roots Ex 3.8 are helpful to complete your math homework.

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RD Sharma Class 8 Solutions Chapter 3 Squares and Square Roots Ex 3.7

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RD Sharma Class 8 Solutions Chapter 3 Squares and Square Roots Ex 3.7

These Solutions are part of RD Sharma Class 8 Solutions. Here we have given RD Sharma Class 8 Solutions Chapter 3 Squares and Square Roots Ex 3.7

Other Exercises

Find the square root of the following numbers in decimal form :

Question 1.
84.8241
Solution:
RD Sharma Class 8 Solutions Chapter 3 Squares and Square Roots Ex 3.7 1

Question 2.
0.7225
Solution:
RD Sharma Class 8 Solutions Chapter 3 Squares and Square Roots Ex 3.7 2

Question 3.
0.813604
Solution:
RD Sharma Class 8 Solutions Chapter 3 Squares and Square Roots Ex 3.7 3
RD Sharma Class 8 Solutions Chapter 3 Squares and Square Roots Ex 3.7 4

Question 4.
0.00002025
Solution:
RD Sharma Class 8 Solutions Chapter 3 Squares and Square Roots Ex 3.7 5

Question 5.
150.0625
Solution:
RD Sharma Class 8 Solutions Chapter 3 Squares and Square Roots Ex 3.7 6

Question 6.
225.6004
Solution:
RD Sharma Class 8 Solutions Chapter 3 Squares and Square Roots Ex 3.7 7

Question 7.
3600.720036
Solution:
RD Sharma Class 8 Solutions Chapter 3 Squares and Square Roots Ex 3.7 8

Question 8.
236.144689
Solution:
RD Sharma Class 8 Solutions Chapter 3 Squares and Square Roots Ex 3.7 9
RD Sharma Class 8 Solutions Chapter 3 Squares and Square Roots Ex 3.7 10

Question 9.
0.00059049
Solution:
RD Sharma Class 8 Solutions Chapter 3 Squares and Square Roots Ex 3.7 11

Question 10.
176.252176
Solution:
RD Sharma Class 8 Solutions Chapter 3 Squares and Square Roots Ex 3.7 12
RD Sharma Class 8 Solutions Chapter 3 Squares and Square Roots Ex 3.7 13

Question 11.
9998.0001
Solution:
RD Sharma Class 8 Solutions Chapter 3 Squares and Square Roots Ex 3.7 14

Question 12.
0.00038809
Solution:
RD Sharma Class 8 Solutions Chapter 3 Squares and Square Roots Ex 3.7 15
RD Sharma Class 8 Solutions Chapter 3 Squares and Square Roots Ex 3.7 16

Question 13.
What is that fraction which when multiplied by itself gives 227.798649 ?
Solution:
RD Sharma Class 8 Solutions Chapter 3 Squares and Square Roots Ex 3.7 17

Question 14.
square playground is 256.6404 square metres. Find the length of one side of the playground.
Solution:
Area of square playground = 256.6404 sq. m
RD Sharma Class 8 Solutions Chapter 3 Squares and Square Roots Ex 3.7 18

Question 15.
What is the fraction which when multiplied by itself gives 0.00053361 ?
Solution:
RD Sharma Class 8 Solutions Chapter 3 Squares and Square Roots Ex 3.7 19

Question 16.
Simplify :
RD Sharma Class 8 Solutions Chapter 3 Squares and Square Roots Ex 3.7 20
RD Sharma Class 8 Solutions Chapter 3 Squares and Square Roots Ex 3.7 21
Solution:
RD Sharma Class 8 Solutions Chapter 3 Squares and Square Roots Ex 3.7 22

Question 17.
Evaluate \(\sqrt { 50625 }\) and hence find the value of \(\sqrt { 506.25 } +\sqrt { 5.0625 } \).
Solution:
RD Sharma Class 8 Solutions Chapter 3 Squares and Square Roots Ex 3.7 23
RD Sharma Class 8 Solutions Chapter 3 Squares and Square Roots Ex 3.7 24

Question 18.
Find the value of \(\sqrt { 103.0225 }\) and hence And the value of
RD Sharma Class 8 Solutions Chapter 3 Squares and Square Roots Ex 3.7 25
Solution:
RD Sharma Class 8 Solutions Chapter 3 Squares and Square Roots Ex 3.7 26

Hope given RD Sharma Class 8 Solutions Chapter 3 Squares and Square Roots Ex 3.7 are helpful to complete your math homework.

If you have any doubts, please comment below. Learn Insta try to provide online math tutoring for you.

RD Sharma Class 8 Solutions Chapter 3 Squares and Square Roots Ex 3.6

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RD Sharma Class 8 Solutions Chapter 3 Squares and Square Roots Ex 3.6

These Solutions are part of RD Sharma Class 8 Solutions. Here we have given RD Sharma Class 8 Solutions Chapter 3 Squares and Square Roots Ex 3.6

Other Exercises

Question 1.
Find the square root of:
RD Sharma Class 8 Solutions Chapter 3 Squares and Square Roots Ex 3.6 1
RD Sharma Class 8 Solutions Chapter 3 Squares and Square Roots Ex 3.6 2
Solution:
RD Sharma Class 8 Solutions Chapter 3 Squares and Square Roots Ex 3.6 3
RD Sharma Class 8 Solutions Chapter 3 Squares and Square Roots Ex 3.6 4
RD Sharma Class 8 Solutions Chapter 3 Squares and Square Roots Ex 3.6 5
RD Sharma Class 8 Solutions Chapter 3 Squares and Square Roots Ex 3.6 6
RD Sharma Class 8 Solutions Chapter 3 Squares and Square Roots Ex 3.6 7
RD Sharma Class 8 Solutions Chapter 3 Squares and Square Roots Ex 3.6 8
RD Sharma Class 8 Solutions Chapter 3 Squares and Square Roots Ex 3.6 9
RD Sharma Class 8 Solutions Chapter 3 Squares and Square Roots Ex 3.6 10
RD Sharma Class 8 Solutions Chapter 3 Squares and Square Roots Ex 3.6 11
RD Sharma Class 8 Solutions Chapter 3 Squares and Square Roots Ex 3.6 12

Question 2.
Find the value of :
RD Sharma Class 8 Solutions Chapter 3 Squares and Square Roots Ex 3.6 13
Solution:
RD Sharma Class 8 Solutions Chapter 3 Squares and Square Roots Ex 3.6 14
RD Sharma Class 8 Solutions Chapter 3 Squares and Square Roots Ex 3.6 15

Question 3.
The area of a square field is 80 \(\frac {244 }{ 729 }\) square metres. Find the length of each side of the field.
Solution:
RD Sharma Class 8 Solutions Chapter 3 Squares and Square Roots Ex 3.6 16

Question 4.
The area of a square field is 30 \(\frac {1 }{ 4}\) m2. Calculate the length of the side of the squre.
Solution:
RD Sharma Class 8 Solutions Chapter 3 Squares and Square Roots Ex 3.6 17

Question 5.
Find the length of a side of a square playground whose area is equal to the area of a rectangular field of dimensions 72 m and 338 m.
Solution:
Length of rectangular field (l) = 338 m
and breadth (b) = 72 m
∴ Area = 1 x 6= 338 x 72 m2
∴ Area of square = 338 x 72 m2 = 24336 m2
and length of the side of the square
RD Sharma Class 8 Solutions Chapter 3 Squares and Square Roots Ex 3.6 18

Hope given RD Sharma Class 8 Solutions Chapter 3 Squares and Square Roots Ex 3.6 are helpful to complete your math homework.

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RD Sharma Class 8 Solutions Chapter 3 Squares and Square Roots Ex 3.5

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RD Sharma Class 8 Solutions Chapter 3 Squares and Square Roots Ex 3.5

These Solutions are part of RD Sharma Class 8 Solutions. Here we have given RD Sharma Class 8 Solutions Chapter 3 Squares and Square Roots Ex 3.5

Other Exercises

Question 1.
Find the square root of each of the long division method.
(I) 12544
(ii) 97344
(iii) 286225
(iv) 390625
(v) 363609
(vi) 974169
(vii) 120409
(viii) 1471369
(ix) 291600
(x) 9653449
(xi) 1745041
(xii) 4008004
(xiii) 20657025
(xiv) 152547201
(jcv) 20421361
(xvi) 62504836
(xvii) 82264900
(xviii) 3226694416
(xix)6407522209
(xx) 3915380329
Solution:
<RD Sharma Class 8 Solutions Chapter 3 Squares and Square Roots Ex 3.5 1
RD Sharma Class 8 Solutions Chapter 3 Squares and Square Roots Ex 3.5 2
RD Sharma Class 8 Solutions Chapter 3 Squares and Square Roots Ex 3.5 3
RD Sharma Class 8 Solutions Chapter 3 Squares and Square Roots Ex 3.5 4

RD Sharma Class 8 Solutions Chapter 3 Squares and Square Roots Ex 3.5 5
RD Sharma Class 8 Solutions Chapter 3 Squares and Square Roots Ex 3.5 6
RD Sharma Class 8 Solutions Chapter 3 Squares and Square Roots Ex 3.5 7
RD Sharma Class 8 Solutions Chapter 3 Squares and Square Roots Ex 3.5 8
RD Sharma Class 8 Solutions Chapter 3 Squares and Square Roots Ex 3.5 9

Question 2.
Find the least number which must be subtracted from the following numbers to make them a perfect square :
(i) 2361
(ii) 194491
(iii) 26535
(iv) 16160
(v) 4401624
Solution:
(i) 2361
Finding the square root of 2361
RD Sharma Class 8 Solutions Chapter 3 Squares and Square Roots Ex 3.5 10
We get 48 as quotient and remainder = 57
∴ To make it a perfect square, we have to subtract 57 from 2361
∴ Least number to be subtracted = 57
(ii) 194491
Finding the square root of 194491
RD Sharma Class 8 Solutions Chapter 3 Squares and Square Roots Ex 3.5 11
We get 441 as quotient and remainder = 10
∴ To make it a perfect square, we have to subtract 10 from 194491
∴ Least number to be subtracted = 10
(iii) 26535
Finding the square root of 26535
RD Sharma Class 8 Solutions Chapter 3 Squares and Square Roots Ex 3.5 12
We get 162 as quotient and 291 as remainder
∴ To make it a perfect square, we have to subtract 291 from 26535
∴ Least number to be subtracted = 291
(iv)16160
Finding the square root of 16160
RD Sharma Class 8 Solutions Chapter 3 Squares and Square Roots Ex 3.5 13
We get 127 as quotient and 31 as remainder
∴ To make it a perfect square, we have to subtract 31 from 16160
∴ Least number to be subtracted = 31
(v) 4401624
Find the square root of 4401624
RD Sharma Class 8 Solutions Chapter 3 Squares and Square Roots Ex 3.5 14
We get 2098 as quotient and 20 as remainder
∴ To make it a perfect square, we have to subtract 20 from 4401624
∴ Least number to be subtracted = 20

Question 3.
Find the least number which must be added to the following numbers to make them a perfect square :
(i) 5607
(ii) 4931
(iii) 4515600
(iv) 37460
(v) 506900
Solution:
(i) 5607
RD Sharma Class 8 Solutions Chapter 3 Squares and Square Roots Ex 3.5 15
Finding the square root of 5607, we see that 742 = 5607- 131 =5476 and 752 = 5625
∴ 5476 < 5607 < 5625
∴ 5625 – 5607 = 18 is to be added to get a perfect square
∴ Least number to be added = 18
(ii) 4931
RD Sharma Class 8 Solutions Chapter 3 Squares and Square Roots Ex 3.5 16
Finding the square root of 4931, we see that 702= 4900
∴ 712 = 5041 4900 <4931 <5041
∴ 5041 – 4931 = 110 is to be added to get a perfect square.
∴ Least number to be added =110
(iii) 4515600
RD Sharma Class 8 Solutions Chapter 3 Squares and Square Roots Ex 3.5 17
Finding the square root of 4515600, we see
that 21242 = 4511376
and 2 1 252 = 45 1 56 25
∴ 4511376 <4515600 <4515625
∴ 4515625 – 4515600 = 25 is to be added to get a perfect square.
∴ Least number to be added = 25
(iv) 37460
RD Sharma Class 8 Solutions Chapter 3 Squares and Square Roots Ex 3.5 18
Finding the square root of 37460
that 1932 = 37249, 1942 = =37636
∴ 37249 < 37460 < 37636
∴ 37636 – 37460 = 176 is to be added to get a perfect square.
∴ Least number to be added =176
(v) 506900
RD Sharma Class 8 Solutions Chapter 3 Squares and Square Roots Ex 3.5 19
Finding the square root of 506900, we see that
7112 = 505521, 7122 = 506944
∴ 505521 < 506900 < 506944
∴ 506944 – 506900 = 44 is to be added to get a perfect square.
∴ Least number to be added = 44

Question 4.
Find the greatest number of 5 digits which is a perfect square.
Solution:
Greatest number of 5-digits = 99999 Finding square root, we see that 143 is left as remainder
RD Sharma Class 8 Solutions Chapter 3 Squares and Square Roots Ex 3.5 20
∴ Perfect square = 99999 – 143 = 99856 If we add 1 to 99999, it will because a number of 6 digits
∴ Greatest square 5-digits perfect square = 99856

Question 5.
Find the least number of four digits which is a perfect square.
Solution:
Least number of 4-digits = 10000
Finding square root of 1000
We see that if we subtract 39
RD Sharma Class 8 Solutions Chapter 3 Squares and Square Roots Ex 3.5 21
From 1000, we get three digit number
∴ We shall add 124 – 100 = 24 to 1000 to get a
perfect square of 4-digit number
∴ 1000 + 24 = 1024
∴ Least number of 4-digits which is a perfect square = 1024

Question 6.
Find the least number of six-digits which is a perfect square.
Solution:
Least number of 6-digits = 100000
RD Sharma Class 8 Solutions Chapter 3 Squares and Square Roots Ex 3.5 22
Finding the square root of 100000, we see that if we subtract 544, we get a perfect square of 5-digits.
So we shall add
4389 – 3900 = 489
to 100000 to get a perfect square
Past perfect square of six digits= 100000 + 489 =100489

Question 7.
Find the greatest number of 4-digits which is a perfect square.
Solution:
Greatest number of 4-digits = 9999
RD Sharma Class 8 Solutions Chapter 3 Squares and Square Roots Ex 3.5 23
Finding the square root, we see that 198 has been left as remainder
∴ 4-digit greatest perfect square = 9999 – 198 = 9801

Question 8.
A General arranges his soldiers in rows to form a perfect square. He finds that in doing so, 60 soldiers are left out. If the total number of soldiers be 8160, find the number of soldiers in each row.
Solution:
Total number of soldiers = 8160 Soldiers left after arranging them in a square = 60
∴ Number of soldiers which are standing in a square = 8160 – 60 = 8100
RD Sharma Class 8 Solutions Chapter 3 Squares and Square Roots Ex 3.5 24

Question 9.
The area of a square field is 60025 m2. A man cycle along its boundry at 18 km/hr. In how much time will be return at the starting point.
Solution:
Area of a square field = 60025 m2
RD Sharma Class 8 Solutions Chapter 3 Squares and Square Roots Ex 3.5 25

Question 10.
The cost of levelling and turfing a square lawn at Rs. 250 per m2 is Rs. 13322.50. Find the cost of fencing it at Rs. 5 per metre ?
Solution:
Cost of levelling a square field = Rs. 13322.50
Rate of levelling = Rs. 2.50 per m2
RD Sharma Class 8 Solutions Chapter 3 Squares and Square Roots Ex 3.5 26
and perimeter = 4a = 4 x 73 = 292 m Rate of fencing the field = Rs. 5 per m
∴ Total cost of fencing = Rs. 5 x 292 = Rs. 1460

Question 11.
Find the greatest number of three digits which is a perfect square.
Solution:
3-digits greatest number = 999
RD Sharma Class 8 Solutions Chapter 3 Squares and Square Roots Ex 3.5 27
Finding the square root, we see that 38 has been left
∴ Perfect square = 999 – 38 = 961
∴ Greatest 3-digit perfect square = 961

Question 12.
Find the smallest number which must be added to 2300 so that it becomes a perfect square.
Solution:
Finding the square root of 2300
RD Sharma Class 8 Solutions Chapter 3 Squares and Square Roots Ex 3.5 28
We see that we have to add 704 – 700 = 4 to 2300 in order to get a perfect square
∴ Smallest number to be added = 4

Hope given RD Sharma Class 8 Solutions Chapter 3 Squares and Square Roots Ex 3.5 are helpful to complete your math homework.

If you have any doubts, please comment below. Learn Insta try to provide online math tutoring for you.