Simplify 4 square root of 2x*5 square root of 6xy^2

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

Step 1

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

Move $x$ .

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

Reorder $6$ and $y^{2}$ .

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

Add parentheses.

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

Step 2

Pull terms out from under the radical.

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

Step 3

Multiply $4 \sqrt{2 x} (5 y \sqrt{6 x})$ .

Multiply $5$ by $4$ .

$20 \sqrt{2 x} (y \sqrt{6 x})$

Combine using the product rule for radicals.

$20 (y \sqrt{2 x (6 x)})$

Multiply $6$ by $2$ .

$20 (y \sqrt{12 x \cdot x})$

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

$20 (y \sqrt{12 (x^{1} x)})$

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

$20 (y \sqrt{12 (x^{1} x^{1})})$

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

$20 (y \sqrt{12 x^{1 + 1}})$

Add $1$ and $1$ .

$20 (y \sqrt{12 x^{2}})$

Step 4

Rewrite $12 x^{2}$ as ${(2 x)}^{2} \cdot 3$ .

Factor $4$ out of $12$ .

$20 (y \sqrt{4 (3) x^{2}})$

Rewrite $4$ as $2^{2}$ .

$20 (y \sqrt{2^{2} \cdot 3 x^{2}})$

Move $3$ .

$20 (y \sqrt{2^{2} x^{2} \cdot 3})$

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

$20 (y \sqrt{{(2 x)}^{2} \cdot 3})$

Step 5

Pull terms out from under the radical.

$20 (y (2 x \sqrt{3}))$

Step 6

Simplify the expression.

Rewrite using the commutative property of multiplication.

$20 (2 \sqrt{3} y x)$

Multiply $2$ by $20$ .

$40 \sqrt{3} y x$

Simplify 4 square root of 2x*5 square root of 6xy^2

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