Simplify ( square root of 8x)(5 square root of 2x)

$(\sqrt{8 x}) (5 \sqrt{2 x})$

Step 1

Rewrite using the commutative property of multiplication.

$5 \sqrt{8 x} \sqrt{2 x}$

Step 2

Rewrite $8 x$ as $2^{2} \cdot (2 x)$ .

Factor $4$ out of $8$ .

$5 \sqrt{4 (2) x} \sqrt{2 x}$

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

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

Add parentheses.

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

Step 3

Pull terms out from under the radical.

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

Step 4

Multiply $2$ by $5$ .

$10 \sqrt{2 x} \sqrt{2 x}$

Step 5

Multiply $10 \sqrt{2 x} \sqrt{2 x}$ .

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

$10 ({\sqrt{2 x}}^{1} \sqrt{2 x})$

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

$10 ({\sqrt{2 x}}^{1} {\sqrt{2 x}}^{1})$

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

$10 {\sqrt{2 x}}^{1 + 1}$

Add $1$ and $1$ .

$10 {\sqrt{2 x}}^{2}$

Step 6

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

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

$10 {({(2 x)}^{\frac{1}{2}})}^{2}$

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

$10 {(2 x)}^{\frac{1}{2} \cdot 2}$

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

$10 {(2 x)}^{\frac{2}{2}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$10 {(2 x)}^{\frac{2}{2}}$

Rewrite the expression.

$10 {(2 x)}^{1}$

Simplify.

$10 (2 x)$

Step 7

Multiply $2$ by $10$ .

$20 x$

Simplify ( square root of 8x)(5 square root of 2x)

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