Question

The value of $\sqrt{1\frac{1}{2}-\left[\begin{array}{c}1\frac{1}{2}-1\frac{1}{2}+\left(\begin{array}{c}1\frac{1}{2}-1\frac{1}{2}-1\frac{1}{4}\end{array}\right)\end{array}\right]}$ is

• A. $\frac{1}{2}$
• B. $\frac{1}{4}$
• C. $\frac{1}{16}$
• D. $1\frac{1}{5}$

Answer 1

The correct option is A $\frac{1}{2}$

$\sqrt{1\frac{1}{2}-\left[\begin{array}{c}1\frac{1}{2}-1\frac{1}{2}+\left(\begin{array}{c}1\frac{1}{2}-1\frac{1}{2}-1\frac{1}{4}\end{array}\right)\end{array}\right]}$
$\Rightarrow \sqrt{\frac{3}{2}-[\frac{3}{2}-\frac{3}{2}+(\frac{3}{2}-\frac{3}{2}-\frac{5}{4})]}$
$\Rightarrow \sqrt{\frac{3}{2}-[0+\left(\frac{6-6-5}{4}\right)]}$
$\Rightarrow \sqrt{\frac{3}{2}-\frac{5}{4}}$
$\Rightarrow \sqrt{\frac{6-5}{4}}$
$\Rightarrow \sqrt{\frac{1}{4}}$
$\Rightarrow \frac{1}{2}$