Basic Math Examples

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

Step 1

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

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Step 1.1

Factor $4$ out of $20$ .

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

Step 1.2

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

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

Step 1.3

Add parentheses.

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

Step 2

Pull terms out from under the radical.

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

Step 3

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

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Step 3.1

Factor out $y^{2}$ .

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

Step 3.2

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

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

Step 3.3

Add parentheses.

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

Step 4

Pull terms out from under the radical.

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

Step 5

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

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Step 5.1

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

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

Step 5.2

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

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

Step 5.3

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

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

Step 5.4

Add $1$ and $1$ .

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

Step 6

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

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Step 6.1

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

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

Step 6.2

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

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

Step 6.3

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

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

Step 6.4

Cancel the common factor of $2$ .

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Step 6.4.1

Cancel the common factor.

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

Step 6.4.2

Rewrite the expression.

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

Step 6.5

Simplify.

$2 (y (5 y))$

Step 7

Multiply $y$ by $y$ by adding the exponents.

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Step 7.1

Move $y$ .

$2 (y \cdot y \cdot 5)$

Step 7.2

Multiply $y$ by $y$ .

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

Step 8

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

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

Step 9

Multiply $5$ by $2$ .

$10 y^{2}$