Evaluate square root of 100/9

$\sqrt{\frac{100}{9}}$

Step 1

Rewrite $\sqrt{\frac{100}{9}}$ as $\frac{\sqrt{100}}{\sqrt{9}}$ .

$\frac{\sqrt{100}}{\sqrt{9}}$

Step 2

Simplify the numerator.

Rewrite $100$ as $10^{2}$ .

$\frac{\sqrt{10^{2}}}{\sqrt{9}}$

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

$\frac{10}{\sqrt{9}}$

Step 3

Simplify the denominator.

Rewrite $9$ as $3^{2}$ .

$\frac{10}{\sqrt{3^{2}}}$

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

$\frac{10}{3}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\frac{10}{3}$

Decimal Form:

$3.\overline{3}$

Mixed Number Form:

$3 \frac{1}{3}$