Simplify square root of 18x* square root of 32x

$\sqrt{18 x} \cdot \sqrt{32 x}$

Step 1

Rewrite $18 x$ as $3^{2} \cdot (2 x)$ .

Factor $9$ out of $18$ .

$\sqrt{9 (2) x} \cdot \sqrt{32 x}$

Rewrite $9$ as $3^{2}$ .

$\sqrt{3^{2} \cdot 2 x} \cdot \sqrt{32 x}$

Add parentheses.

$\sqrt{3^{2} \cdot (2 x)} \cdot \sqrt{32 x}$

Step 2

Pull terms out from under the radical.

$3 \sqrt{2 x} \cdot \sqrt{32 x}$

Step 3

Rewrite $32 x$ as ${(2^{2})}^{2} \cdot (2 x)$ .

Factor $16$ out of $32$ .

$3 \sqrt{2 x} \cdot \sqrt{16 (2) x}$

Rewrite $16$ as $4^{2}$ .

$3 \sqrt{2 x} \cdot \sqrt{4^{2} \cdot 2 x}$

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

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

Add parentheses.

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

Step 4

Pull terms out from under the radical.

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

Step 5

Raise $2$ to the power of $2$ .

$3 \sqrt{2 x} \cdot (4 \sqrt{2 x})$

Step 6

Multiply $3 \sqrt{2 x} (4 \sqrt{2 x})$ .

Multiply $4$ by $3$ .

$12 \sqrt{2 x} \sqrt{2 x}$

Raise $\sqrt{2 x}$ to the power of $1$ .

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

Raise $\sqrt{2 x}$ to the power of $1$ .

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

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

$12 {\sqrt{2 x}}^{1 + 1}$

Add $1$ and $1$ .

$12 {\sqrt{2 x}}^{2}$

Step 7

Rewrite ${\sqrt{2 x}}^{2}$ as $2 x$ .

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{2 x}$ as ${(2 x)}^{\frac{1}{2}}$ .

$12 {({(2 x)}^{\frac{1}{2}})}^{2}$

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$12 {(2 x)}^{\frac{1}{2} \cdot 2}$

Combine $\frac{1}{2}$ and $2$ .

$12 {(2 x)}^{\frac{2}{2}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$12 {(2 x)}^{\frac{2}{2}}$

Rewrite the expression.

$12 {(2 x)}^{1}$

Simplify.

$12 (2 x)$

Step 8

Multiply $2$ by $12$ .

$24 x$

Simplify square root of 18x* square root of 32x

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