Simplify square root of (225x^3)/(49x)

$\sqrt{\frac{225 x^{3}}{49 x}}$

Step 1

Reduce the expression $\frac{225 x^{3}}{49 x}$ by cancelling the common factors.

Factor $x$ out of $225 x^{3}$ .

$\sqrt{\frac{x (225 x^{2})}{49 x}}$

Factor $x$ out of $49 x$ .

$\sqrt{\frac{x (225 x^{2})}{x \cdot 49}}$

Cancel the common factor.

$\sqrt{\frac{x (225 x^{2})}{x \cdot 49}}$

Rewrite the expression.

$\sqrt{\frac{225 x^{2}}{49}}$

Step 2

Rewrite $225 x^{2}$ as ${(15 x)}^{2}$ .

$\sqrt{\frac{{(15 x)}^{2}}{49}}$

Step 3

Rewrite $49$ as $7^{2}$ .

$\sqrt{\frac{{(15 x)}^{2}}{7^{2}}}$

Step 4

Rewrite $\frac{{(15 x)}^{2}}{7^{2}}$ as ${(\frac{15 x}{7})}^{2}$ .

$\sqrt{{(\frac{15 x}{7})}^{2}}$

Step 5

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

$\frac{15 x}{7}$