Simplify square root of 20x* square root of 5x^3

$\sqrt{20 x} \cdot \sqrt{5 x^{3}}$

Step 1

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

Factor $4$ out of $20$ .

$\sqrt{4 (5) x} \cdot \sqrt{5 x^{3}}$

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

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

Add parentheses.

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

Step 2

Pull terms out from under the radical.

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

Step 3

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

Factor out $x^{2}$ .

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

Reorder $5$ and $x^{2}$ .

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

Add parentheses.

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

Step 4

Pull terms out from under the radical.

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

Step 5

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

Raise $\sqrt{5 x}$ to the power of $1$ .

$2 (x ({\sqrt{5 x}}^{1} \sqrt{5 x}))$

Raise $\sqrt{5 x}$ to the power of $1$ .

$2 (x ({\sqrt{5 x}}^{1} {\sqrt{5 x}}^{1}))$

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

$2 (x {\sqrt{5 x}}^{1 + 1})$

Add $1$ and $1$ .

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

Step 6

Rewrite ${\sqrt{5 x}}^{2}$ as $5 x$ .

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{5 x}$ as ${(5 x)}^{\frac{1}{2}}$ .

$2 (x {({(5 x)}^{\frac{1}{2}})}^{2})$

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

$2 (x {(5 x)}^{\frac{1}{2} \cdot 2})$

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

$2 (x {(5 x)}^{\frac{2}{2}})$

Cancel the common factor of $2$ .

Cancel the common factor.

$2 (x {(5 x)}^{\frac{2}{2}})$

Rewrite the expression.

$2 (x {(5 x)}^{1})$

Simplify.

$2 (x (5 x))$

Step 7

Multiply $x$ by $x$ by adding the exponents.

Move $x$ .

$2 (x \cdot x \cdot 5)$

Multiply $x$ by $x$ .

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

Step 8

Move $5$ to the left of $x^{2}$ .

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

Step 9

Multiply $5$ by $2$ .

$10 x^{2}$

Simplify square root of 20x* square root of 5x^3

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