Question

Identify the following as rational or irrational numbers. Give the decimal representation of rational numbers :

(i) $\sqrt{4}$ (ii) $3\sqrt{18}$

(iii) $\sqrt{1.44}$ (iv) $\sqrt{\frac{9}{27}}$

(v) $-\sqrt{64}$ (vi) $\sqrt{100}$

Answer 1

(i) $\sqrt{4}$ = 2

It is a rational number.

(ii) $3\sqrt{18}$ = 3 $\times \sqrt{9\times 2}=3\times 3\sqrt{2}=9\sqrt{2}$

It is a irrational number.

(iii) $\sqrt{1.44}$ = $\sqrt{1.2\times 1.2}$ = 1.2

It is a rational number.

(iv) $\sqrt{\frac{9}{27}}=\sqrt{\frac{1}{3}}=\sqrt{1}\sqrt{3}$

=$\frac{1\times \sqrt{3}}{\sqrt{3}\times \sqrt{3}}=\frac{\sqrt{3}}{3}$

It is an irrational number.

(v) $-\sqrt{64}$ = $-\sqrt{8\times 8}=-8$

It is a rational number.

(vi) $\sqrt{100}=\sqrt{10\times 10}=10$