Question

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 1

(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.