Simplify square root of (9x^4)/36

$\sqrt{\frac{9 x^{4}}{36}}$

Step 1

Reduce the expression $\frac{9 x^{4}}{36}$ by cancelling the common factors.

Factor $9$ out of $9 x^{4}$ .

$\sqrt{\frac{9 (x^{4})}{36}}$

Factor $9$ out of $36$ .

$\sqrt{\frac{9 x^{4}}{9 \cdot 4}}$

Cancel the common factor.

$\sqrt{\frac{9 x^{4}}{9 \cdot 4}}$

Rewrite the expression.

$\sqrt{\frac{x^{4}}{4}}$

Step 2

Simplify the expression.

Rewrite $x^{4}$ as ${(x^{2})}^{2}$ .

$\sqrt{\frac{{(x^{2})}^{2}}{4}}$

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

$\sqrt{\frac{{(x^{2})}^{2}}{2^{2}}}$

Step 3

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

$\sqrt{{(\frac{x^{2}}{2})}^{2}}$

Step 4

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

$\frac{x^{2}}{2}$