Simplify square root of 15x* square root of 20xy

$\sqrt{15 x} \cdot \sqrt{20 x y}$

Step 1

Rewrite $20 x y$ as $2^{2} \cdot (5 x y)$ .

Factor $4$ out of $20$ .

$\sqrt{15 x} \cdot \sqrt{4 (5) x y}$

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

$\sqrt{15 x} \cdot \sqrt{2^{2} \cdot 5 x y}$

Add parentheses.

$\sqrt{15 x} \cdot \sqrt{2^{2} \cdot 5 (x y)}$

Add parentheses.

$\sqrt{15 x} \cdot \sqrt{2^{2} \cdot (5 x y)}$

Step 2

Pull terms out from under the radical.

$\sqrt{15 x} \cdot (2 \sqrt{5 x y})$

Step 3

Rewrite using the commutative property of multiplication.

$2 \sqrt{15 x} \sqrt{5 x y}$

Step 4

Multiply $2 \sqrt{15 x} \sqrt{5 x y}$ .

Combine using the product rule for radicals.

$2 \sqrt{5 x y (15 x)}$

Multiply $15$ by $5$ .

$2 \sqrt{75 x y x}$

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

$2 \sqrt{75 (x^{1} x) y}$

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

$2 \sqrt{75 (x^{1} x^{1}) y}$

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

$2 \sqrt{75 x^{1 + 1} y}$

Add $1$ and $1$ .

$2 \sqrt{75 x^{2} y}$

Step 5

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

Factor $25$ out of $75$ .

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

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

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

Move $3$ .

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

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

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

Add parentheses.

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

Step 6

Pull terms out from under the radical.

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

Step 7

Multiply $5$ by $2$ .

$10 x \sqrt{3 y}$

Simplify square root of 15x* square root of 20xy

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