Question

Simplify:
(i) $\frac{{11}^{\frac{1}{2}}}{{11}^{\frac{1}{4}}}$ (ii) $7^{\frac{1}{2}}{.8}^{\frac{1}{2}}$
[2 Marks]
[RS Aggarwal]
[Operations on Real Numbers]

Answer 1

Solution:

(i) $\frac{{11}^{\frac{1}{2}}}{{11}^{\frac{1}{4}}}={11}^{\frac{1}{2}-\frac{1}{4}}[\because \frac{a^m}{a^n}=a^{m-n}]$ .
$={11}^{\frac{2-1}{4}}$
$={11}^{\frac{1}{4}}$
[1 Mark]

(ii) $7^{\frac{1}{2}}{.8}^{\frac{1}{2}}$
$=(7\times 8{)}^{\frac{1}{2}}[\because a^m.b^m=\left(ab{)}^m\right]={56}^{\frac{1}{2}}$
[1 Mark]