# Without a calculator, is there a way to have sqrt(3) as a result when calculating this: (2)sqrt(3/4) ?

Apr 7, 2018

Yes. See below.

#### Explanation:

$\implies 2 \sqrt{\frac{3}{4}}$

$\implies \frac{2 \sqrt{3}}{\sqrt{4}}$

=> (2sqrt(3))/(sqrt(2^(2))

=> (cancel(2) sqrt(3)) / cancel(2) color(white)(..)[∵ sqrt(2^2) = 2]

$\implies \sqrt{3}$

Apr 7, 2018

We know that the square root of $4$ is $2$.
Also, $\sqrt{\frac{3}{4}}$ can be decomposed as $\frac{\sqrt{3}}{\sqrt{4}}$.