Evaluate square root of 81/4

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

Step 1

Rewrite $\sqrt{\frac{81}{4}}$ as $\frac{\sqrt{81}}{\sqrt{4}}$ .

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

Step 2

Simplify the numerator.

Rewrite $81$ as $9^{2}$ .

$\frac{\sqrt{9^{2}}}{\sqrt{4}}$

Pull terms out from under the radical, assuming positive real numbers.

$\frac{9}{\sqrt{4}}$

Step 3

Simplify the denominator.

Rewrite $4$ as $2^{2}$ .

$\frac{9}{\sqrt{2^{2}}}$

Pull terms out from under the radical, assuming positive real numbers.

$\frac{9}{2}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\frac{9}{2}$

Decimal Form:

$4.5$

Mixed Number Form:

$4 \frac{1}{2}$