Question

Simplify the expression.

$\sqrt{\frac{15}{16}}$

Short answer

The simplified value is$\frac{\sqrt{3\times 5}}{4}$.

Step-by-step solution

Step 1. Given Information.

The given expression is$\sqrt{\frac{15}{16}}$ .

Step 2. Calculation.

The expression can be simplified as,

$\begin{array}{c}\sqrt{\frac{15}{16}}=\frac{\sqrt{15}}{\sqrt{16}}\\ =\frac{{\left(15\right)}^{\frac{1}{2}}}{{\left(16\right)}^{\frac{1}{2}}}\\ =\frac{{(3\times 5)}^{\frac{1}{2}}}{{\left(4^2\right)}^{\frac{1}{2}}}\\ =\frac{\sqrt{3\times 5}}{4}\end{array}$

Step 3. Conclusion.

The simplified value of the given expression is$\frac{\sqrt{3\times 5}}{4}$ .