Evaluate square root of 125/45

$\sqrt{\frac{125}{45}}$

Step 1

Cancel the common factor of $125$ and $45$ .

Factor $5$ out of $125$ .

$\sqrt{\frac{5 (25)}{45}}$

Cancel the common factors.

Factor $5$ out of $45$ .

$\sqrt{\frac{5 \cdot 25}{5 \cdot 9}}$

Cancel the common factor.

$\sqrt{\frac{5 \cdot 25}{5 \cdot 9}}$

Rewrite the expression.

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

Step 2

Rewrite $\sqrt{\frac{25}{9}}$ as $\frac{\sqrt{25}}{\sqrt{9}}$ .

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

Step 3

Simplify the numerator.

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

$\frac{\sqrt{5^{2}}}{\sqrt{9}}$

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

$\frac{5}{\sqrt{9}}$

Step 4

Simplify the denominator.

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

$\frac{5}{\sqrt{3^{2}}}$

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

$\frac{5}{3}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{5}{3}$

Decimal Form:

$1.\overline{6}$

Mixed Number Form:

$1 \frac{2}{3}$