Simplify 6xy^3 square root of 75x^5y^4

$6 x y^{3} \sqrt{75 x^{5} y^{4}}$

Rewrite $75 x^{5} y^{4}$ as ${(5 x^{2} y^{2})}^{2} \cdot (3 x)$ .

Factor $25$ out of $75$ .

$6 x y^{3} \sqrt{25 (3) x^{5} y^{4}}$

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

$6 x y^{3} \sqrt{5^{2} \cdot 3 x^{5} y^{4}}$

Factor out $x^{4}$ .

$6 x y^{3} \sqrt{5^{2} \cdot 3 (x^{4} x) y^{4}}$

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

$6 x y^{3} \sqrt{5^{2} \cdot 3 ({(x^{2})}^{2} x) y^{4}}$

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

$6 x y^{3} \sqrt{5^{2} \cdot 3 ({(x^{2})}^{2} x) {(y^{2})}^{2}}$

Move $x$ .

$6 x y^{3} \sqrt{5^{2} \cdot 3 ({(x^{2})}^{2}) {(y^{2})}^{2} x}$

Move $3$ .

$6 x y^{3} \sqrt{(5^{2} ({(x^{2})}^{2})) {(y^{2})}^{2} \cdot 3 x}$

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

$6 x y^{3} \sqrt{{(5 x^{2} y^{2})}^{2} \cdot 3 x}$

Add parentheses.

$6 x y^{3} \sqrt{{(5 x^{2} y^{2})}^{2} \cdot (3 x)}$

Pull terms out from under the radical.

$6 x y^{3} (5 x^{2} y^{2} \sqrt{3 x})$

Multiply $x$ by $x^{2}$ by adding the exponents.

Move $x^{2}$ .

$6 (x^{2} x) y^{3} (5 y^{2} \sqrt{3 x})$

Multiply $x^{2}$ by $x$ .

Raise $x$ to the power of $1$ .

$6 (x^{2} x^{1}) y^{3} (5 y^{2} \sqrt{3 x})$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$6 x^{2 + 1} y^{3} (5 y^{2} \sqrt{3 x})$

Add $2$ and $1$ .

$6 x^{3} y^{3} (5 y^{2} \sqrt{3 x})$

Multiply $y^{3}$ by $y^{2}$ by adding the exponents.

Move $y^{2}$ .

$6 x^{3} (y^{2} y^{3}) (5 \sqrt{3 x})$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$6 x^{3} y^{2 + 3} (5 \sqrt{3 x})$

Add $2$ and $3$ .

$6 x^{3} y^{5} (5 \sqrt{3 x})$

Multiply $5$ by $6$ .

$30 x^{3} y^{5} \sqrt{3 x}$