Simplify square root of 75x^3

$\sqrt{75 x^{3}}$

Step 1

Rewrite $75 x^{3}$ as ${(5 x)}^{2} \cdot (3 x)$ .

Factor $25$ out of $75$ .

$\sqrt{25 (3) x^{3}}$

Rewrite $25$ as $5^{2}$ .

$\sqrt{5^{2} \cdot 3 x^{3}}$

Factor out $x^{2}$ .

$\sqrt{5^{2} \cdot 3 (x^{2} x)}$

Move $3$ .

$\sqrt{5^{2} x^{2} \cdot 3 x}$

Rewrite $5^{2} x^{2}$ as ${(5 x)}^{2}$ .

$\sqrt{{(5 x)}^{2} \cdot 3 x}$

Add parentheses.

$\sqrt{{(5 x)}^{2} \cdot (3 x)}$

$\sqrt{{(5 x)}^{2} \cdot (3 x)}$

Step 2

Pull terms out from under the radical.

$5 x \sqrt{3 x}$

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