Simplify square root of (7x^5)/(63x)

$\sqrt{\frac{7 x^{5}}{63 x}}$

Step 1

Reduce the expression $\frac{7 x^{5}}{63 x}$ by cancelling the common factors.

Factor $7$ out of $7 x^{5}$ .

$\sqrt{\frac{7 (x^{5})}{63 x}}$

Factor $7$ out of $63 x$ .

$\sqrt{\frac{7 (x^{5})}{7 (9 x)}}$

Cancel the common factor.

$\sqrt{\frac{7 x^{5}}{7 (9 x)}}$

Rewrite the expression.

$\sqrt{\frac{x^{5}}{9 x}}$

Step 2

Cancel the common factor of $x^{5}$ and $x$ .

Factor $x$ out of $x^{5}$ .

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

Cancel the common factors.

Factor $x$ out of $9 x$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Step 3

Simplify the expression.

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

$\sqrt{\frac{{(x^{2})}^{2}}{9}}$

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

$\sqrt{\frac{{(x^{2})}^{2}}{3^{2}}}$

Step 4

Rewrite $\frac{{(x^{2})}^{2}}{3^{2}}$ as ${(\frac{x^{2}}{3})}^{2}$ .

$\sqrt{{(\frac{x^{2}}{3})}^{2}}$

Step 5

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

$\frac{x^{2}}{3}$