Simplify square root of 75x^3- square root of 27x^3

$\sqrt{75 x^{3}} - \sqrt{27 x^{3}}$

Step 1

Simplify each term.

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

Factor $25$ out of $75$ .

$\sqrt{25 (3) x^{3}} - \sqrt{27 x^{3}}$

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

$\sqrt{5^{2} \cdot 3 x^{3}} - \sqrt{27 x^{3}}$

Factor out $x^{2}$ .

$\sqrt{5^{2} \cdot 3 (x^{2} x)} - \sqrt{27 x^{3}}$

Move $3$ .

$\sqrt{5^{2} x^{2} \cdot 3 x} - \sqrt{27 x^{3}}$

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

$\sqrt{{(5 x)}^{2} \cdot 3 x} - \sqrt{27 x^{3}}$

Add parentheses.

$\sqrt{{(5 x)}^{2} \cdot (3 x)} - \sqrt{27 x^{3}}$

Pull terms out from under the radical.

$5 x \sqrt{3 x} - \sqrt{27 x^{3}}$

Rewrite $27 x^{3}$ as ${(3 x)}^{2} \cdot (3 x)$ .

Factor $9$ out of $27$ .

$5 x \sqrt{3 x} - \sqrt{9 (3) x^{3}}$

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

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

Factor out $x^{2}$ .

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

Move $3$ .

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

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

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

Add parentheses.

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

Pull terms out from under the radical.

$5 x \sqrt{3 x} - (3 x \sqrt{3 x})$

Multiply $3$ by $- 1$ .

$5 x \sqrt{3 x} - 3 x \sqrt{3 x}$

Step 2

Subtract $3 x \sqrt{3 x}$ from $5 x \sqrt{3 x}$ .

$2 x \sqrt{3 x}$