ICSE

ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 3 Squares and Square Roots Ex 3.4

Question 1.
Find the square root of each of the following by division method:
(i) 2401
(ii) 4489
(iii) 106929
(iv) 167281
(v) 53824
(vi) 213444
Solution:

Question 2.
Find the number of digits in the square root of each of the following (without any calculation):
(i) 81
(ii) 169
(iii) 4761
(iv) 27889
(v) 525625
Solution:

Question 3.
Find the square root of the following decimal numbers by division method:
(i) 51.84
(ii) 42.25
(iii) 18.4041
(iv) 5.774409
Solution:

Question 4.
Find the square root of the following numbers correct to two decimal places:
(i) 645.8
(ii) 107.45
(iii) 5.462
(iv) 2
(v) 3
Solution:

Question 5.
Find the square root of the following fractions by division method:

Solution:

Question 6.
Find the least number which must be subtracted from each of the following numbers to make them a perfect square. Also find the square root of the perfect square number so obtained:
(i) 2000
(ii) 984
(iii) 8934
(iv) 11021
Solution:

Question 7.
Find the least number which must be added to each of the following numbers to make them a perfect square. Also find the square root of the perfect square number so obtained:
(i) 1750
(ii) 6412
(iii) 6598
(iv) 8000
Solution:

Question 8.
Find the smallest four-digit number which is a perfect square.
Solution:

Question 9.
Find the greatest number of six digits which is a perfect square.
Solution:

Question 10.
In a right triangle ABC, ∠B = 90°.
(i) If AB = 14 cm, BC = 48 cm, find AC.
(ii) If AC = 37 cm, BC = 35 cm, find AB.
Solution:

Question 11.
A gardener has 1400 plants. He wants to plant these in such a way that the number of rows and number of columns remains the same. Find the minimum number of plants he needs more for this.
Solution:

Question 12.
There are 1000 children in a school. For a P.T. drill they have to stand in such a way that the number of rows is equal to a number of columns. How many children would be left out in this arrangement?
Solution:

Question 13.
Amit walks 16 m south from his house and turns east to walk 63 ra to reach his friend’s house. While returning, he walks diagonally from his friend’s house to reach back to his house. What distance did he walk while returning?
Solution:

Question 14.
A ladder 6 m long leaned against a wall. The ladder reaches the wall to a height of 4.8 m. Find the distance between the wall and the foot of the ladder.
Solution:

ML Aggarwal Class 8 Solutions for ICSE Maths

ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 3 Squares and Square Roots Ex 3.3

Question 1.
By repeated subtraction of odd numbers starting from 1, find whether the following numbers are perfect squares or not? If the number is a perfect square then find its square root:
(i) 121
(ii) 55
(iii) 36
(iv) 90
Solution:

Question 2.
Find the square roots of the following numbers by prime factorisation method:
(i) 784
(ii) 441
(iii) 1849
(iv) 4356
(v) 6241
(vi) 8836
(vii) 8281
(viii) 9025
Solution:

Question 3.
Find the square roots of the following numbers by prime factorisation method:

Solution:

Question 4.
For each of the following numbers, find the smallest natural number by which it should be multiplied so as to get a perfect square. Also, find the square root of the square number so obtained:
(i) 588
(ii) 720
(iii) 2178
(iv) 3042
(v) 6300
Solution:

Question 5.
For each of the following numbers, find the smallest natural number by which it should be divided so that this quotient is a perfect square. Also, find the square root of the square number so obtained:
(i) 1872
(ii) 2592
(iii) 3380
(iv) 16224
(v) 61347
Solution:

Question 6.
Find the smallest square number that is divisible by each of the following numbers:
(i) 3, 6, 10, 15
(ii) 6, 9, 27, 36
(iii) 4, 7, 8, 16
Solution:

Question 7.
4225 plants are to be planted in a garden in such a way that each row contains as many plants as the number of rows. Find the number of rows and the number of plants in each row.
Solution:

Question 8.
The area of a rectangle is 1936 sq. m. If the length of the rectangle is 4 times its breadth, find the dimensions of the rectangle.
Solution:

Question 9.
In a school a P.T. teacher wants to arrange 2000 students in the form of rows and columns for P.T. display. If the number of rows is equal to number of columns and 64 students could not be accommodated in this arrangement. Find the number of rows.
Solution:

Question 10.
In a school, the students of class VIII collected ₹2304 for a picnic. Each student contributed as mdny rupees as the number of students in the class. Find the number of students in the class.
Solution:

Question 11.
The product of two numbers is 7260. If one number is 15 times the other number, find the numbers.
Solution:

Question 12.
Find three positive numbers in the ratio 2 : 3 : 5, the sum of whose squares is 950.
Solution:

Question 13.
The perimeter of two squares is 60 metres and 144 metres respectively. Find the perimeter of another square equal in area to the sum of the first two squares.
Solution:

ML Aggarwal Class 8 Solutions for ICSE Maths

ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 3 Squares and Square Roots Ex 3.2

Question 1.
Write five numbers which you can decide by looking at their one’s digit that they are not square numbers.
Solution:

Question 2.
What will be the unit digit of the squares of the following numbers?
(i) 951
(ii) 502
(iii) 329
(iv) 643
(v) 5124
(vi) 7625
(vii) 68327
(viii) 95628
(ix) 99880
(x) 12796
Solution:

Question 3.
The following numbers are obviously not perfect. Give reason.
(i) 567
(ii) 2453
(iii) 5298
(iv) 46292
(v) 74000
Solution:

Question 4.
The square of which of the following numbers would be an odd number or an even number? Why?
(i) 573
(ii) 4096
(iii) 8267
(iv) 37916
Solution:

Question 5.
How many natural numbers lie between the square of the following numbers?
(i) 12 and 13
(ii) 90 and 91
Solution:

Question 6.
Without adding, find the sum.
(i) 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15
(ii) 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19 + 21 + 23 + 25 + 27 + 29
Solution:

Question 7.
(i) Express 64 as the sum of 8 odd numbers.
(ii) 121 as the sum of 11 odd numbers.
Solution:

Question 8.
Express the following as the sum of two consecutive integers:
(i) 19²
(ii) 33²
(iii) 47²
Solution:

Question 9.
Find the squares of the following numbers without actual multiplication:
(i) 31
(ii) 42
(iii) 86
(iv) 94
Solution:

Question 10.
Find the squares of the following numbers containing 5 in unit’s place:
(i) 45
(ii) 305
(iii) 525
Solution:

Question 11.
Write a Pythagorean triplet whose one number is
(i) 8
(ii) 15
(iii) 63
(iv) 80
Solution:

Question 12.
Observe the following pattern and find the missing digits:
21² = 441
201² = 40401
2001² = 4004001
20001² = 4 – – – 4 – – – 1
200001² = ————–
Solution:

Question 13.
Observe the following pattern and find the missing digits:
9² = 81
99² = 9801
999² = 998001
9999² = 99980001
99999² = 9——–8———01
999999² = 9——–0———1
Solution:

Question 14.
Observe the following pattern and find the missing digits:
7² = 49
67² = 4489
667² = 444889
6667² = 44448889
66667² = 4 ———–8 ————– 9
666667² = 4———–8————8 –
Solution:

ML Aggarwal Class 8 Solutions for ICSE Maths

ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 3 Squares and Square Roots Ex 3.1

Question 1.
Which of the following natural numbers are perfect squares? Give reasons in support of your answer.
(i) 729
(ii) 5488
(iii) 1024
(iv) 243
Solution:

Question 2.
Show that each of the following numbers is a perfect square. Also, find the number whose square is the given number.
(i) 1296
(ii) 1764
(iii) 3025
(iv) 3969
Solution:

Question 3.
Find the smallest natural number by which 1008 should be multiplied to make it a perfect square.
Solution:

Question 4.
Find the smallest natural number by which 5808 should be divided to make it a perfect square. Also, find the number whose square is the resulting number.
Solution:

ML Aggarwal Class 8 Solutions for ICSE Maths

ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 2 Exponents and Powers Check Your Progress

Question 1.
Evaluate:

Solution:

Question 2.
Simplify:

Solution:

Question 3.
Find the multiplicative inverse of \(\left(\frac{125}{27}\right)^{\frac{-2}{3}}\)
Solution:

Question 4.
Simplify and write in exponential form:

Solution:

Question 5.
Simplify: \(\frac{5^{n+2}-6+5^{n+1}}{13 \times 5^{n}-2 \times 5^{n+1}}\)
Solution:

Question 6.
Prove that (a + b)^-1 (a^-1 + b^-1) = (ab)^-1.
Solution:

Question 7.
Find the value of x for which

Solution:

Question 8.
If \(\frac{2^{-n} \times 8^{2 n+1} \times 16^{2 n}}{4^{3 n}}=\frac{1}{16}\), find the value of n.
Solution:

Question 9.
By what number should \(\left[\left(\frac{-5}{2}\right)^{3}\right]^{-3}\) be multiplied to get \(\left(\frac{-2}{5}\right)^{5}\)?
Solution:

Question 10.
By what number should \(\left(\frac{-3}{2}\right)^{-4}\) be divided to get \(\left(\frac{-2}{3}\right)^{3}\)?
Solution:

Question 11.
Express the following numbers in standard form:
(i) 0.0000000003904
(ii) 12730000000000
Solution:

Question 12.
Express the following numbers in the usual form:
(i) 5.73 × 10^-11
(ii) 3.895 × 10¹⁵.
Solution:

Question 13.
If \(\left(\frac{9}{4}\right)^{-4} \times\left(\frac{2}{3}\right)^{3}=\left(\frac{p}{q}\right)^{11}\), then find the value of \(\left(\frac{p}{q}\right)^{-2}\).
Solution:

Question 14.
Mass of the Earth is 5.97 × 10²⁴ kg and mass of the Moon is 7.35 × 10²² kg. What is the difference of their masses?
Solution:

ML Aggarwal Class 8 Solutions for ICSE Maths