Simplify (15 square root of 90)/( square root of 125)

$\frac{15 \sqrt{90}}{\sqrt{125}}$

Combine $\sqrt{90}$ and $\sqrt{125}$ into a single radical.

$15 \sqrt{\frac{90}{125}}$

Cancel the common factor of $90$ and $125$ .

Factor $5$ out of $90$ .

$15 \sqrt{\frac{5 (18)}{125}}$

Cancel the common factors.

Factor $5$ out of $125$ .

$15 \sqrt{\frac{5 \cdot 18}{5 \cdot 25}}$

Cancel the common factor.

$15 \sqrt{\frac{5 \cdot 18}{5 \cdot 25}}$

Rewrite the expression.

$15 \sqrt{\frac{18}{25}}$

Rewrite $\sqrt{\frac{18}{25}}$ as $\frac{\sqrt{18}}{\sqrt{25}}$ .

$15 \frac{\sqrt{18}}{\sqrt{25}}$

Simplify the numerator.

Rewrite $18$ as $3^{2} \cdot 2$ .

Factor $9$ out of $18$ .

$15 \frac{\sqrt{9 (2)}}{\sqrt{25}}$

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

$15 \frac{\sqrt{3^{2} \cdot 2}}{\sqrt{25}}$

Pull terms out from under the radical.

$15 \frac{3 \sqrt{2}}{\sqrt{25}}$

Simplify the denominator.

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

$15 \frac{3 \sqrt{2}}{\sqrt{5^{2}}}$

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

$15 \frac{3 \sqrt{2}}{5}$

Reduce the expression by cancelling the common factors.

Cancel the common factor of $5$ .

Factor $5$ out of $15$ .

$5 (3) \frac{3 \sqrt{2}}{5}$

Cancel the common factor.

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

Rewrite the expression.

$3 (3 \sqrt{2})$

Multiply $3$ by $3$ .

$9 \sqrt{2}$

The result can be shown in multiple forms.

Exact Form:

$9 \sqrt{2}$

Decimal Form:

$12.72792206 \dots$