R.d Sharma 2022 _mcqs for Class 9 Maths Chapter 3 - Rationalisation

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R.d Sharma 2022 _mcqs Solutions for Class 9 Maths Chapter 3 Rationalisation are provided here with simple step-by-step explanations. These solutions for Rationalisation are extremely popular among Class 9 students for Maths Rationalisation Solutions come handy for quickly completing your homework and preparing for exams. All questions and answers from the R.d Sharma 2022 _mcqs Book of Class 9 Maths Chapter 3 are provided here for you for free. You will also love the ad-free experience on Meritnation’s R.d Sharma 2022 _mcqs Solutions. All R.d Sharma 2022 _mcqs Solutions for class Class 9 Maths are prepared by experts and are 100% accurate.

Page No 36:

Question 1:

$\sqrt{10} \times \sqrt{15}$ is equal to

(a) 5 $\sqrt{6}$

(b) 6 $\sqrt{5}$

(c) $\sqrt{30}$

(d) $\sqrt{25}$

Answer:

Given that, it can be simplified as

Therefore given expression is simplified and correct choice is

Page No 36:

Question 2:

$\sqrt[5]{6} \times \sqrt[5]{6}$ is equal to

(a) $\sqrt[5]{36}$

(b) $\sqrt[5]{6 \times 0}$

(c) $\sqrt[5]{6}$

(d) $\sqrt[5]{12}$

Answer:

Given that, it can be simplified as

Therefore given expression is simplified and correct choice is.

Page No 36:

Question 3:

The rationalisation factor of $\sqrt{3}$ is

(a) $- \sqrt{3}$

(b) $\frac{1}{\sqrt{3}}$

(c) $2 \sqrt{3}$

(d) $- 2 \sqrt{3}$

Answer:

We know that rationalization factor for is. Hence rationalization factor of is.Hence the correct option is.

Page No 36:

Question 4:

The rationalisation factor of $2 + \sqrt{3}$ , is

(a) $2 - \sqrt{3}$

(b) $2 + \sqrt{3}$

(c) $\sqrt{2} - 3$

(d) $\sqrt{3} - 2$

Answer:

We know that rationalization factor for is. Hence rationalization factor of is.Hence correct option is

Page No 36:

Question 5:

If x = $\sqrt{5} + 2$ , then $x - \frac{1}{x}$ equals

(a) $2 \sqrt{5}$

(b) 4

(c) 2

(d) $\sqrt{5}$

Answer:

Given that.Hence is given as

.We need to find

We know that rationalization factor for is. We will multiply numerator and denominator of the given expression by, to get

Therefore,

Hence the correct option is.

Page No 36:

Question 6:

If $\frac{\sqrt{3 - 1}}{\sqrt{3} + 1}$ = $a - b \sqrt{3}$ , then

(a) a = 2, b =1

(b) a = 2, b =−1

(c) a = −2, b = 1

(d) a = b = 1

Answer:

Given that:

We are asked to find a and b

We know that rationalization factor for is . We will multiply numerator and denominator of the given expression by, to get

On equating rational and irrational terms, we get

Comparing rational and irrational part we get

Hence, the correct choice is.

Page No 36:

Question 7:

The simplest rationalising factor of $\sqrt{3} + \sqrt{5}$ , is

(a) $\sqrt{3} - 5$

(b) $3 - \sqrt{5}$

(c) $\sqrt{3} - \sqrt{5}$

(d) $\sqrt{3} + \sqrt{5}$

Answer:

We know that rationalization factor for is. Hence rationalization factor of is.

Page No 36:

Question 8:

The simplest rationalising factor of $2 \sqrt{5}$ − $\sqrt{3}$ is

(a) $2 \sqrt{5} + 3$

(b) $2 \sqrt{5} + \sqrt{3}$

(c) $\sqrt{5} + \sqrt{3}$

(d) $\sqrt{5} - \sqrt{3}$

Answer:

We know that rationalization factor for is. Hence rationalization factor of is.

Page No 37:

Question 9:

If x = $\frac{2}{3 + \sqrt{7}}$ , then (x−3)² =

(a) 1
(b) 3
(c) 6
(d) 7

Answer:

Given that:

We know that rationalization factor for is. We will multiply numerator and denominator of the given expression by, to get

Therefore,

On squaring both sides, we get

Hence the value of the given expression is.

Page No 37:

Question 10:

If $x = 7 + 4 \sqrt{3}$ and xy =1, then $\frac{1}{x^{2}} + \frac{1}{y^{2}} =$

(a) 64

(b) 134

(c) 194

(d) $\frac{1}{49}$

Answer:

Given that,

Hence is given as

We need to find

We know that rationalization factor for is. We will multiply numerator and denominator of the given expression by, to get

Since so we have

Therefore,

Hence the value of the given expression is.

Page No 37:

Question 11:

If $x + \sqrt{15} = 4,$ then $x + \frac{1}{x}$ =

(a) 2
(b) 4
(c) 8
(d) 1

Answer:

Given that .It can be simplified as

We need to find

We know that rationalization factor for is. We will multiply numerator and denominator of the given expression by, to get

Therefore,

Hence the value of the given expression is 8.Hence correct option is .

Page No 37:

Question 12:

If $x = \frac{\sqrt{5} + \sqrt{3}}{\sqrt{5} - \sqrt{3}}$ and $y = \frac{\sqrt{5} - \sqrt{3}}{\sqrt{5} + \sqrt{3}}$ , then x + y +xy=

(a) 9
(b) 5
(c) 17
(d) 7

Answer:

Given that and.

We are asked to find

Now we will rationalize x. We know that rationalization factor for is. We will multiply numerator and denominator of the given expression by, to get

Similarly, we can rationalize y. We know that rationalization factor for is. We will multiply numerator and denominator of the given expression by, to get

Therefore,

Hence the value of the given expression is.

Page No 37:

Question 13:

If x= $\frac{\sqrt{3} - \sqrt{2}}{\sqrt{3} + \sqrt{2}}$ and y = $\frac{\sqrt{3} + \sqrt{2}}{\sqrt{3} - \sqrt{2}}$ , then x² + y +y² =

(a) 101
(b) 99
(c) 98
(d) 102

Answer:

Given that and.

We need to find

Now we will rationalize x. We know that rationalization factor for is. We will multiply numerator and denominator of the given expression by, to get

Similarly, we can rationalize y. We know that rationalization factor for is. We will multiply numerator and denominator of the given expression by, to get

Therefore,

Hence the value of the given expression is.

Page No 37:

Question 14:

$\frac{1}{\sqrt{9} - \sqrt{8}}$ is equal to

(a) $3 + 2 \sqrt{2}$

(b) $\frac{1}{3 + 2 \sqrt{2}}$

(c) $3 - 2 \sqrt{2}$

(d) $\frac{3}{2} - \sqrt{2}$

Answer:

Given that

We know that rationalization factor for is. We will multiply numerator and denominator of the given expression by, to get

Hence the correct option is.

Page No 37:

Question 15:

If $\frac{5 - \sqrt{3}}{2 + \sqrt{3}} = x + y \sqrt{3}$ , then

(a) x = 13, y = −7

(b) x = −13, y = 7

(c) x = −13, y = −7

(d) x = 13, y = 7

Answer:

Given that: .We need to find x and y

We know that rationalization factor for is . We will multiply numerator and denominator of the given expression by, to get

Since

On equating rational and irrational terms, we get

Hence, the correct choice is.

Page No 37:

Question 16:

If x = $\sqrt[3]{2 + \sqrt{3}}$ , then $x^{3} + \frac{1}{x^{3}} =$

(a) 2

(b) 4

(c) 8

(d) 9

Answer:

Given that .It can be simplified as

We know that rationalization factor for is. We will multiply numerator and denominator of the given expression by, to get

Therefore,

Hence the value of the given expression is.

Page No 37:

Question 17:

The value of $\sqrt{3 - 2 \sqrt{2}}$ is

(a) $\sqrt{2} - 1$

(b) $\sqrt{2} + 1$

(c) $\sqrt{3} - \sqrt{2}$

(d) $\sqrt{3} + \sqrt{2}$

Answer:

Given that:.It can be written in the form as

Hence the value of the given expression is.

Page No 37:

Question 18:

The value of $\sqrt{5 + 2 \sqrt{6}}$ ,is

(a) $\sqrt{3} - \sqrt{2}$

(b) $\sqrt{3} + \sqrt{2}$

(c) $\sqrt{5} + \sqrt{6}$

(d) none of these

Answer:

Given that:.It can be written in the form as

Hence the value of the given expression is.

Page No 37:

Question 19:

If $\sqrt{2} = 1.4142$ then $\sqrt{\frac{\sqrt{2} - 1}{\sqrt{2} + 1}}$ is equal to

(a) 0.1718

(b) 5.8282

(c) 0.4142

(d) 2.4142

Answer:

Given that , we need to find the value of .

We can rationalize the denominator of the given expression. We know that rationalization factor for is. We will multiply numerator and denominator of the given expression by, to get

$\sqrt{\frac{\sqrt{2} - 1}{\sqrt{2} + 1}} = \frac{\sqrt{2} - 1}{1}$

Putting the value of , we get

Hence the value of the given expression is 0.14142 and correct choice is.

Page No 37:

Question 20:

If $\sqrt{2} = 1.414,$ then the value of $\sqrt{6} - \sqrt{3}$ upto three places of decimal is

(a) 0.235

(b) 0.707

(c) 1.414

(d) 0.471

Answer:

Given that.We need to find.

We can factor out from the given expression, to get

Putting the value of, we get

Hence the value of expression must closely resemble be

The correct option is.

Page No 37:

Question 21:

The positive square root of $7 + \sqrt{48}$ is

(a) $7 + 2 \sqrt{3}$

(b) $7 + \sqrt{3}$

(c) $2 + \sqrt{3}$

(d) $3 + \sqrt{2}$

Answer:

Given that:.To find square root of the given expression we need to rewrite the expression in the form

Hence the square root of the given expression is

Hence the correct option is.

Page No 37:

Question 22:

If $x = \sqrt{6} + \sqrt{5}$ , then $x^{2} + \frac{1}{x^{2}} - 2 =$

(a) $2 \sqrt{6}$

(b) $2 \sqrt{5}$

(c) 24

(d) 20

Answer:

Given that.Hence is given as

We need to find

We know that rationalization factor for is. We will multiply numerator and denominator of the given expression by, to get

We know that therefore,

Hence the value of the given expression is 20 and correct option is (d).

Page No 38:

Question 23:

If $\sqrt{13 - a \sqrt{10}} = \sqrt{8} + \sqrt{5}, then a =$

(a) −5

(b) −6

(c) −4

(d) −2

Answer:

Given that:

We need to find a

The given expression can be simplified by taking square on both sides

The irrational terms on right side can be factorized such that it of the same form as left side terms.

Hence,

On comparing rational and irrational terms, we get.Therefore, correct choice is .

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