Question

Simplify the expression.

$\sqrt{\frac{81}{4}}$

Short answer

The simplified value is$\frac{9}{2}$.

Step-by-step solution

Step 1. Given Information.

The given expression is$\sqrt{\frac{81}{4}}$.

Step 2. Calculation.

The expression can be simplified as,

$\begin{array}{c}\sqrt{\frac{81}{4}}=\frac{\sqrt{81}}{\sqrt{4}}\\ =\frac{{\left(81\right)}^{\frac{1}{2}}}{{\left(4\right)}^{\frac{1}{2}}}\\ =\frac{{\left(9^2\right)}^{\frac{1}{2}}}{{\left(2^2\right)}^{\frac{1}{2}}}\\ =\frac{9}{2}\end{array}$

Step 3. Conclusion.

The simplified value of the given expression is$\frac{9}{2}$.