Simplify ( square root of 30x^3y^2)( square root of 5x^4y^3)

$(\sqrt{30 x^{3} y^{2}}) (\sqrt{5 x^{4} y^{3}})$

Rewrite $30 x^{3} y^{2}$ as ${(x y)}^{2} \cdot (30 x)$ .

Factor out $x^{2}$ .

$\sqrt{30 (x^{2} x) y^{2}} \sqrt{5 x^{4} y^{3}}$

Move $x$ .

$\sqrt{30 (x^{2}) y^{2} x} \sqrt{5 x^{4} y^{3}}$

Move $30$ .

$\sqrt{(x^{2}) y^{2} \cdot 30 x} \sqrt{5 x^{4} y^{3}}$

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

$\sqrt{{(x y)}^{2} \cdot 30 x} \sqrt{5 x^{4} y^{3}}$

Add parentheses.

$\sqrt{{(x y)}^{2} \cdot (30 x)} \sqrt{5 x^{4} y^{3}}$

Pull terms out from under the radical.

$x y \sqrt{30 x} \sqrt{5 x^{4} y^{3}}$

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

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

$x y \sqrt{30 x} \sqrt{5 {(x^{2})}^{2} y^{3}}$

Factor out $y^{2}$ .

$x y \sqrt{30 x} \sqrt{5 {(x^{2})}^{2} (y^{2} y)}$

Move $5$ .

$x y \sqrt{30 x} \sqrt{{(x^{2})}^{2} y^{2} \cdot 5 y}$

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

$x y \sqrt{30 x} \sqrt{{(x^{2} y)}^{2} \cdot 5 y}$

Add parentheses.

$x y \sqrt{30 x} \sqrt{{(x^{2} y)}^{2} \cdot (5 y)}$

Pull terms out from under the radical.

$x y \sqrt{30 x} (x^{2} y \sqrt{5 y})$

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

Move $x^{2}$ .

$x^{2} x y \sqrt{30 x} (y \sqrt{5 y})$

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

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

$x^{2} x^{1} y \sqrt{30 x} (y \sqrt{5 y})$

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

$x^{2 + 1} y \sqrt{30 x} (y \sqrt{5 y})$

Add $2$ and $1$ .

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

Multiply $y$ by $y$ by adding the exponents.

Move $y$ .

$x^{3} (y \cdot y) \sqrt{30 x} \sqrt{5 y}$

Multiply $y$ by $y$ .

$x^{3} y^{2} \sqrt{30 x} \sqrt{5 y}$

Multiply $x^{3} y^{2} \sqrt{30 x} \sqrt{5 y}$ .

Combine using the product rule for radicals.

$x^{3} y^{2} \sqrt{5 y (30 x)}$

Multiply $30$ by $5$ .

$x^{3} y^{2} \sqrt{150 y x}$

Rewrite $150 y x$ as $5^{2} \cdot (6 y x)$ .

Factor $25$ out of $150$ .

$x^{3} y^{2} \sqrt{25 (6) y x}$

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

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

Add parentheses.

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

Add parentheses.

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

Pull terms out from under the radical.

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

Rewrite using the commutative property of multiplication.

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

Simplify ( square root of 30x^3y^2)( square root of 5x^4y^3)

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