Simplify square root of 72xy* square root of 4xy^2

$\sqrt{72 x y} \cdot \sqrt{4 x y^{2}}$

Step 1

Rewrite $72 x y$ as $6^{2} \cdot (2 x y)$ .

Factor $36$ out of $72$ .

$\sqrt{36 (2) x y} \cdot \sqrt{4 x y^{2}}$

Rewrite $36$ as $6^{2}$ .

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

Add parentheses.

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

Add parentheses.

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

Step 2

Pull terms out from under the radical.

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

Step 3

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

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

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

Move $x$ .

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

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

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

Step 4

Pull terms out from under the radical.

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

Step 5

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

Multiply $2$ by $6$ .

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

Combine using the product rule for radicals.

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

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

$12 (y \sqrt{2 (x^{1} x) y})$

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

$12 (y \sqrt{2 (x^{1} x^{1}) y})$

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

$12 (y \sqrt{2 x^{1 + 1} y})$

Add $1$ and $1$ .

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

Step 6

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

Reorder $2$ and $x^{2}$ .

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

Add parentheses.

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

Step 7

Pull terms out from under the radical.

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

Step 8

Reorder factors in $12 y (x \sqrt{2 y})$ .

$12 y x \sqrt{2 y}$

Simplify square root of 72xy* square root of 4xy^2

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