CBSE Class 9

RD Sharma Class 9 Solutions Chapter 3 Rationalisation Ex 3.1

These Solutions are part of RD Sharma Class 9 Solutions. Here we have given RD Sharma Class 9 Solutions Chapter 3 Rationalisation Ex 3.1

Question 1.
Simplify each of the following:

Solution:

Question 2.
Simplify the following expressions:
(i)  (4 + \(\sqrt { 7 } \)) (3 + \(\sqrt { 2 } \))
(ii) (3 + \(\sqrt { 3 } \) )(5- \(\sqrt { 2 } \))
(iii) (\(\sqrt { 5 } \) -2)(\(\sqrt { 3 } \) – \(\sqrt { 5 } \))
Solution:

Question 3.
Simplify the following expressions:
(i)  (11 + \(\sqrt { 11 } \)) (11 – \(\sqrt { 11 } \))
(ii) (5 + \(\sqrt { 7 } \) ) (5 – \(\sqrt { 7 } \) )
(iii) (\(\sqrt { 8 } \) – \(\sqrt { 2 } \)) (\(\sqrt { 8 } \)+ \(\sqrt { 2 } \))
Solution:

Question 4.
Simplify the following expressions:
(i) (\(\sqrt { 3 } \)+\(\sqrt { 7 } \))²
(ii) (\(\sqrt { 5 } \) – \(\sqrt { 3 } \) )²
(iii) (2\(\sqrt { 5 } \) + 3 \(\sqrt { 2} \))²
Solution:
(i)


Hope given RD Sharma Class 9 Solutions Chapter 3 Rationalisation Ex 3.1 are helpful to complete your math homework.

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RD Sharma Class 9 Solutions Chapter 2 Exponents of Real Numbers MCQS

These Solutions are part of RD Sharma Class 9 Solutions. Here we have given RD Sharma Class 9 Solutions Chapter 2 Exponents of Real Numbers MCQS

Mark the correct alternative in each of the following:
Question 1.
The value of {2 – 3 (2 – 3)³}³ is
(a) 5
(b) 125
(c) \(\frac { 1 }{ 5 }\)
(d) -125
Solution:
{2 – 3 (2 – 3)³}³ = {2 – 3 (-1)³}³
= {2 – 3 x (-1)}³
= (2 + 3)³ = (5)³
= 125    (b)

Question 2.
The value of x – y^x-y when x = 2 and y = -2 is
(a) 18
(b) -18
(c) 14
(d) -14
Solution:
x = 2, y = -2
x-y^x-y = 2 – (-2)^{2 – (-2)}
= 2 – (-2)^{2 + 2} = 2 – (-2)⁴
= 2 – (+16) = 2 – 16 = -14        (d)

Question 3.
The product of the square root of x with the cube root of x, is
(a) cube root of the square root of x
(b) sixth root of the fifth power of x
(c) fifth root of the sixth power of x
(d) sixth root of x
Solution:

Question 4.
The seventh root of x divided by the eighth root of x is

Solution:

Question 5.
The square root of 64 divided by the cube root of 64 is
(a) 64
(b) 2
(c) \(\frac { 1 }{ 2 }\)
(d) 64^{\(\frac { 2 }{ 3 }\)}
Solution:

Question 6.
Which of the following is (are) not equal to

Solution:

Question 7.
When simplified (x^–1 + y^–1)^–1 is equal to

Solution:

Question 8.
If 8^x+1 = 64, what is the value of 3 ^{2x +1}?
(a) 1
(b) 3
(c) 9
(d) 27
Solution:

Question 9.
If (2³)² = 4^x then   3^x =
(a) 3
(b) 6
(c) 9
(d) 27
Solution:

Question 10.
If x^-2= 64, then x^{\(\frac { 1 }{ 3 }\)} + x°=
(a) 2
(b) 3
(c) \(\frac { 3 }{ 2 }\)
(c) \(\frac { 2 }{ 3 }\)
Solution:

Question 11.
When simplified ( –\(\frac { 1 }{ 27 }\))^{\(\frac { -2 }{ 3 }\)}
(a) 9
(b) -9
(c) \(\frac { 1 }{ 9 }\)
(d) –\(\frac { 1 }{ 9 }\)
Solution:

Question 12.
Which one of the following is not equal to

Solution:

Question 13.
Which one of the following is not equal to

Solution:

Question 14.
If a, b, c are positive real numbers, then

Solution:

Question 15.

Solution:

Question 16.

Solution:

Question 17.

Solution:

Question 18.

Solution:

Question 19.

Solution:

Question 20.

Solution:

Question 21.
The value of {(23 + 2²)^2/3+ (150 -29)^1/2}²  is
(a) 196
(b) 289
(c) 324
(d) 400
Solution:
{(23 + 2²)^2/3 + (150 – 29)^1/2}²
= [(23×4)^{\(\frac { 2 }{ 3 }\)}  +(150 – 29)^{\(\frac { 1 }{ 2 }\)} ]²
= [(27)^{\(\frac { 2 }{ 3 }\)} + (121)^{\(\frac { 1 }{ 2 }\)} ]²
= [(3³)³ +(11²)^{\(\frac { 1 }{ 2 }\)}]² = (9 + 11)²
= (20)² = 400  (d)

Question 22.
(256)^0.16x (256)^0.09
(a) 4
(b) 16
(c) 64
(d) 256.25
Solution:

Question 23.
If 10^2y = 25, then 10^-y equals

Solution:

Question 24.
If 9^{X + 2} = 240 + 9^X. then x =
(a) 0.5
(b) 0.2
(c) 0.4
(d) 0.1
Solution:

Question 25.
If x is a positive real number and x² = 2, then x³ =
(a) \(\sqrt { 2 } \)
(b) 2\(\sqrt { 2 } \)
(c) 3\(\sqrt { 2 } \)
(d) 4
Solution:

Question 26.

Solution:

Question 27.

Solution:

Question 28.

Solution:

Question 29.

Solution:

Question 30.

Solution:

Question 31.

Solution:

Question 32.

Solution:

Question 33.
If (16)^{2x + 3} = (64)^{x + 3} , then 4^{2x – 2}  =
(a) 64
(b) 256
(c) 32
(d) 512
Solution:

Question 34.

Solution:

Question 35.

Solution:

Question 36.

Solution:

Question 37.

Solution:

Question 38.

Solution:

Question 39.

Solution:

Question 40.

Solution:

Hope given RD Sharma Class 9 Solutions Chapter 2 Exponents of Real Numbers MCQS 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.