Simplify square root of 81/16

$\sqrt{\frac{81}{16}}$

Step 1

Rewrite $\sqrt{\frac{81}{16}}$ as $\frac{\sqrt{81}}{\sqrt{16}}$ .

$\frac{\sqrt{81}}{\sqrt{16}}$

Step 2

Simplify the numerator.

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

$\frac{\sqrt{9^{2}}}{\sqrt{16}}$

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

$\frac{9}{\sqrt{16}}$

Step 3

Simplify the denominator.

Rewrite $16$ as $4^{2}$ .

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

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

$\frac{9}{4}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\frac{9}{4}$

Decimal Form:

$2.25$

Mixed Number Form:

$2 \frac{1}{4}$