Simplify square root of (7a^3b^4)/(175ab)

$\sqrt{\frac{7 a^{3} b^{4}}{175 a b}}$

Reduce the expression $\frac{7 a^{3} b^{4}}{175 a b}$ by cancelling the common factors.

Factor $7$ out of $7 a^{3} b^{4}$ .

$\sqrt{\frac{7 (a^{3} b^{4})}{175 a b}}$

Factor $7$ out of $175 a b$ .

$\sqrt{\frac{7 (a^{3} b^{4})}{7 (25 a b)}}$

Cancel the common factor.

$\sqrt{\frac{7 (a^{3} b^{4})}{7 (25 a b)}}$

Rewrite the expression.

$\sqrt{\frac{a^{3} b^{4}}{25 a b}}$

Cancel the common factor of $a^{3}$ and $a$ .

Factor $a$ out of $a^{3} b^{4}$ .

$\sqrt{\frac{a (a^{2} b^{4})}{25 a b}}$

Cancel the common factors.

Factor $a$ out of $25 a b$ .

$\sqrt{\frac{a (a^{2} b^{4})}{a (25 b)}}$

Cancel the common factor.

$\sqrt{\frac{a (a^{2} b^{4})}{a (25 b)}}$

Rewrite the expression.

$\sqrt{\frac{a^{2} b^{4}}{25 b}}$

Cancel the common factor of $b^{4}$ and $b$ .

Factor $b$ out of $a^{2} b^{4}$ .

$\sqrt{\frac{b (a^{2} b^{3})}{25 b}}$

Cancel the common factors.

Factor $b$ out of $25 b$ .

$\sqrt{\frac{b (a^{2} b^{3})}{b \cdot 25}}$

Cancel the common factor.

$\sqrt{\frac{b (a^{2} b^{3})}{b \cdot 25}}$

Rewrite the expression.

$\sqrt{\frac{a^{2} b^{3}}{25}}$

Rewrite $\frac{a^{2} b^{3}}{25}$ as ${(\frac{a b}{5})}^{2} b$ .

Factor the perfect power ${(a b)}^{2}$ out of $a^{2} b^{3}$ .

$\sqrt{\frac{{(a b)}^{2} b}{25}}$

Factor the perfect power $5^{2}$ out of $25$ .

$\sqrt{\frac{{(a b)}^{2} b}{5^{2} \cdot 1}}$

Rearrange the fraction $\frac{{(a b)}^{2} b}{5^{2} \cdot 1}$ .

$\sqrt{{(\frac{a b}{5})}^{2} b}$

Pull terms out from under the radical.

$\frac{a b}{5} \sqrt{b}$

Combine $\frac{a b}{5}$ and $\sqrt{b}$ .

$\frac{a b \sqrt{b}}{5}$