RD Sharma Class 9 Solutions Chapter 3 Rationalisation

RD Sharma Class 9 Chapter 3 Rationalisation Ex 3.1

Question 1.
Simplify each of the following:

Solution:

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

Question 3.
Simplify the following expressions:
(i)  (11 + 11−−√) (11 – 11−−√)
(ii) (5 + 7–√ ) (5 – 7–√ )
(iii) (8–√ – 2–√) (8–√+ 2–√)
Solution:

Question 4.
Simplify the following expressions:
(i) (3–√+7–√)²
(ii) (5–√ – 3–√ )²
(iii) (25–√ + 3 2–√)²
Solution:

RD Sharma Solutions Class 9 Chapter 3 Rationalisation Ex 3.2

Question 1.
Rationalise the denominators of each of the following(i – vii):

Solution:

Question 2.
Find the value to three places of decimals of each of the following. It is given that

Solution:

Question 3.
Express each one of the following with rational denominator:

Solution:

Question 4.
Rationales the denominator and simplify:

Solution:

Question 5.
Simplify:

Solution:

Question 6.
In each of the following determine rational numbers a and b:


Solution:

Question 7.

Solution:

Question 8.
Find the values of each of the following correct to three places of decimals, it being given that 2–√  = 1.4142, 3–√ = 1-732, 5–√  = 2.2360, 6–√ =  2.4495 and 10−−√  = 3.162.

Solution:

Question 9.
Simplify:

Solution:

Question 10.

Solution:

Question 11.

Solution:

Question 12.

Solution:

Class 9 RD Sharma Solutions Chapter 3 Rationalisation VSAQS

Question 1.
Write the value of (2 + 3–√ ) (2 – 3–√).
Solution:
(2+ 3–√ )(2- 3–√ ) = (2)²-(3–√ )²
{∵ (a + b) (a – b) = a² – b²}
= 4-3=1

Question 2.
Write the reciprocal of 5 + 2–√.
Solution:

Question 3.
Write the rationalisation factor of 7 – 35–√ .
Solution:
Rationalising factor of 7 – 35–√ is 7 + 35–√
{∵ (a−−√ + b√  ) (a−−√ – b√) = a-b}

Question 4.

Solution:

Question 5.
If x =2–√ – 1 then write the value of 1x.
Solution:

Question 6.
If a = 2–√ + h then find the value of a –1a
Solution:

Question 7.
If x = 2 + 3–√, find the value of x + 1x.
Solution:

Question 8.
Write the rationalisation factor of 5–√ – 2.
Solution:
Rationalisation factor of 5–√ – 2 is 5–√ + 2 as
(a−−√ + b√)(a−−√ – b√) = a – b

Question 9.
Simplify : 3+22–√−−−−−−−√.
Solution:

Question 10.
Simplify : 3−22–√−−−−−−−√.
Solution:

Question 11.
If x = 3 + 2 2–√, then find the value of  x−−√ – 1x√.
Solution:

Rationalisation Problems With Solutions PDF RD Sharma Class 9 Solutions MCQS

Mark the correct alternative in each of the following:

Question 1.

Solution:

Question 2.

Solution:

Question 3.

Solution:

Question 4.
The rationalisation factor of 2 + 3–√  is
(a) 2 – 3–√
(b) 2–√ + 3
(c)  2–√ – 3
(d) 3–√ – 2
Solution:

Question 5.

Solution:

Question 6.

Solution:

Question 7.

Solution:

Question 8.

Solution:

Question 9.

Solution:

Question 10.

Solution:

Question 11.

Solution:

Question 12.

Solution:

Question 13.

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Question 14.

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Question 15.

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Question 16.

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Question 17.

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Question 18.

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Question 19.

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Question 20.

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Question 21.

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Question 22.

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Question 23.

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Question 24.

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Question 25.

Solution: