Simplify square root of 125/9

$\sqrt{\frac{125}{9}}$

Step 1

Rewrite $\sqrt{\frac{125}{9}}$ as $\frac{\sqrt{125}}{\sqrt{9}}$ .

$\frac{\sqrt{125}}{\sqrt{9}}$

Step 2

Simplify the numerator.

Rewrite $125$ as $5^{2} \cdot 5$ .

Factor $25$ out of $125$ .

$\frac{\sqrt{25 (5)}}{\sqrt{9}}$

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

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

Pull terms out from under the radical.

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

Step 3

Simplify the denominator.

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

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

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

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

Step 4

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$3.72677996 \dots$