RD Sharma 2020 solution class 9 chapter 3 Rationalisation Exercise 3.1

Exercise 3.1

Page-3.2

Question 1:

Simplify each of the following:

(i) $\sqrt[3]{4}\times \sqrt[3]{16}$

(ii) $\frac{\sqrt[4]{1250}}{\sqrt[4]{2}}$

Answer 1:

(i) We know that. We will use this property to simplify the expression.

Hence the value of the given expression is .

(ii) We know that. We will use this property to simplify the expression.

Hence the value of the given expression is.

Question 2:

Simplify the following expressions:

(i) $\left(4+\sqrt{7}) (3+\sqrt{2}\right)$

(ii) $\left(3+\sqrt{3}) (5-\sqrt{2}\right)$

(iii) $\left(\sqrt{5}-2) (\sqrt{3}-\sqrt{5}\right)$

Answer 2:

(i) We can simplify the expression as 

Hence the value of the expression is

(ii) We can simplify the expression as 

Hence the value of the expression is

(iii) We can simplify the expression as 

Hence the value of the expression is .

Question 3:

Simplify the following expressions:

(i) $\left(11+\sqrt{11}\right) \left(11-\sqrt{11}\right)$

(ii) $\left(5+\sqrt{7}\right) \left(5-\sqrt{7}\right)$

(iii) $\left(\sqrt{8}-\sqrt{2}\right) \left(\sqrt{8}+\sqrt{2}\right)$

(iv) $\left(3+\sqrt{3}\right)\left(3-\sqrt{3}\right)$

(v) $\left(\sqrt{5}-\sqrt{2}\right) \left(\sqrt{5}+\sqrt{2}\right)$

Answer 3:

(i) We know that. We will use this property to simplify the expression.

Hence the value of expression is 110.

 

(ii) We know that. We will use this property to simplify the expression.

Hence the value of expression is 18.

(iii) We know that. We will use this property to simplify the expression.

Hence the value of expression is 6

(iv) We know that. We will use this property to simplify the expression.

Hence the value of expression is 6.

(v) We know that. We will use this property to simplify the expression.

Hence the value of expression is 3.

Page-3.3

Question 4:

Simplify the following expressions:

(i) ${\left(\sqrt{3}+\sqrt{7}\right)}^2$

(ii) ${\left(\sqrt{5}-\sqrt{3}\right)}^2$

(iii) ${\left(2\sqrt{5}+3\sqrt{2}\right)}^2$

Answer 4:

(i) We know that. We will use this property to simplify the expression.

Hence the value of expression is

(ii) We know that. We will use this property to simplify the expression.

Hence the value of expression is

(iii) We know that. We will use this property to simplify the expression.

Hence the value of expression is.