Evaluate square root of 100/225

$\sqrt{\frac{100}{225}}$

Cancel the common factor of $100$ and $225$ .

Factor $25$ out of $100$ .

$\sqrt{\frac{25 (4)}{225}}$

Cancel the common factors.

Factor $25$ out of $225$ .

$\sqrt{\frac{25 \cdot 4}{25 \cdot 9}}$

Cancel the common factor.

$\sqrt{\frac{25 \cdot 4}{25 \cdot 9}}$

Rewrite the expression.

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

Rewrite $\sqrt{\frac{4}{9}}$ as $\frac{\sqrt{4}}{\sqrt{9}}$ .

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

Simplify the numerator.

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

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

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

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

Simplify the denominator.

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

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

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

$\frac{2}{3}$

The result can be shown in multiple forms.

Exact Form:

$\frac{2}{3}$

Decimal Form:

$0.\overline{6}$