Simplify 6 square root of 18y-3 square root of 32y

$6 \sqrt{18 y} - 3 \sqrt{32 y}$

Step 1

Simplify each term.

Rewrite

$18 y$ as

$3^{2} \cdot (2 y)$ .

Factor

$9$ out of

$18$ .

$6 \sqrt{9 (2) y} - 3 \sqrt{32 y}$

Rewrite

$9$ as

$3^{2}$ .

$6 \sqrt{3^{2} \cdot 2 y} - 3 \sqrt{32 y}$

Add parentheses.

$6 \sqrt{3^{2} \cdot (2 y)} - 3 \sqrt{32 y}$

Pull terms out from under the radical.

$6 (3 \sqrt{2 y}) - 3 \sqrt{32 y}$

Multiply

$3$ by

$6$ .

$18 \sqrt{2 y} - 3 \sqrt{32 y}$

Rewrite

$32 y$ as

${(2^{2})}^{2} \cdot (2 y)$ .

Factor

$16$ out of

$32$ .

$18 \sqrt{2 y} - 3 \sqrt{16 (2) y}$

Rewrite

$16$ as

$4^{2}$ .

$18 \sqrt{2 y} - 3 \sqrt{4^{2} \cdot 2 y}$

Rewrite

$4$ as

$2^{2}$ .

$18 \sqrt{2 y} - 3 \sqrt{{(2^{2})}^{2} \cdot 2 y}$

Add parentheses.

$18 \sqrt{2 y} - 3 \sqrt{{(2^{2})}^{2} \cdot (2 y)}$

Pull terms out from under the radical.

$18 \sqrt{2 y} - 3 (2^{2} \sqrt{2 y})$

Raise

$2$ to the power of

$2$ .

$18 \sqrt{2 y} - 3 (4 \sqrt{2 y})$

Multiply

$4$ by

$- 3$ .

$18 \sqrt{2 y} - 12 \sqrt{2 y}$

Step 2

Subtract

$12 \sqrt{2 y}$ from

$18 \sqrt{2 y}$ .

$6 \sqrt{2 y}$

Simplify 6 square root of 18y-3 square root of 32y

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