Simplify square root of (4a^4b^2)/(16a^2)

$\sqrt{\frac{4 a^{4} b^{2}}{16 a^{2}}}$

Reduce the expression $\frac{4 a^{4} b^{2}}{16 a^{2}}$ by cancelling the common factors.

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

$\sqrt{\frac{4 (a^{4} b^{2})}{16 a^{2}}}$

Factor $4$ out of $16 a^{2}$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Cancel the common factor of $a^{4}$ and $a^{2}$ .

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

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

Cancel the common factors.

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

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

Cancel the common factor.

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

Rewrite the expression.

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

Rewrite $a^{2} b^{2}$ as ${(a b)}^{2}$ .

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

Rewrite $4$ as $2^{2}$ .

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

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

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

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

$\frac{a b}{2}$