Evaluate square root of 1 9/16

$\sqrt{1 \frac{9}{16}}$

Step 1

Convert $1 \frac{9}{16}$ to an improper fraction.

A mixed number is an addition of its whole and fractional parts.

$\sqrt{1 + \frac{9}{16}}$

Add $1$ and $\frac{9}{16}$ .

Write $1$ as a fraction with a common denominator.

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

Combine the numerators over the common denominator.

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

Add $16$ and $9$ .

$\sqrt{\frac{25}{16}}$

Step 2

Rewrite $\sqrt{\frac{25}{16}}$ as $\frac{\sqrt{25}}{\sqrt{16}}$ .

$\frac{\sqrt{25}}{\sqrt{16}}$

Step 3

Simplify the numerator.

Rewrite $25$ as $5^{2}$ .

$\frac{\sqrt{5^{2}}}{\sqrt{16}}$

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

$\frac{5}{\sqrt{16}}$

Step 4

Simplify the denominator.

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

$\frac{5}{\sqrt{4^{2}}}$

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

$\frac{5}{4}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{5}{4}$

Decimal Form:

$1.25$

Mixed Number Form:

$1 \frac{1}{4}$