Simplify square root of 225/625*(m^4n^6)

$\sqrt{\frac{225}{625} \cdot (m^{4} n^{6})}$

Step 1

Combine $\frac{225}{625}$ and $m^{4}$ .

$\sqrt{\frac{225 m^{4}}{625} n^{6}}$

Step 2

Combine $\frac{225 m^{4}}{625}$ and $n^{6}$ .

$\sqrt{\frac{225 m^{4} n^{6}}{625}}$

Step 3

Reduce the expression $\frac{225 m^{4} n^{6}}{625}$ by cancelling the common factors.

Factor $25$ out of $225 m^{4} n^{6}$ .

$\sqrt{\frac{25 (9 m^{4} n^{6})}{625}}$

Factor $25$ out of $625$ .

$\sqrt{\frac{25 (9 m^{4} n^{6})}{25 (25)}}$

Cancel the common factor.

$\sqrt{\frac{25 (9 m^{4} n^{6})}{25 \cdot 25}}$

Rewrite the expression.

$\sqrt{\frac{9 m^{4} n^{6}}{25}}$

Step 4

Rewrite $9 m^{4} n^{6}$ as ${(3 m^{2} n^{3})}^{2}$ .

$\sqrt{\frac{{(3 m^{2} n^{3})}^{2}}{25}}$

Step 5

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

$\sqrt{\frac{{(3 m^{2} n^{3})}^{2}}{5^{2}}}$

Step 6

Rewrite $\frac{{(3 m^{2} n^{3})}^{2}}{5^{2}}$ as ${(\frac{3 m^{2} n^{3}}{5})}^{2}$ .

$\sqrt{{(\frac{3 m^{2} n^{3}}{5})}^{2}}$

Step 7

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

$\frac{3 m^{2} n^{3}}{5}$