Basic Math Examples

$4 \sqrt{80} \cdot \sqrt{20}$

Step 1

Rewrite $80$ as $4^{2} \cdot 5$ .

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Step 1.1

Factor $16$ out of $80$ .

$4 \sqrt{16 (5)} \cdot \sqrt{20}$

Step 1.2

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

$4 \sqrt{4^{2} \cdot 5} \cdot \sqrt{20}$

Step 2

Pull terms out from under the radical.

$4 (4 \sqrt{5}) \cdot \sqrt{20}$

Step 3

Multiply $4$ by $4$ .

$16 \sqrt{5} \cdot \sqrt{20}$

Step 4

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

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Step 4.1

Factor $4$ out of $20$ .

$16 \sqrt{5} \cdot \sqrt{4 (5)}$

Step 4.2

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

$16 \sqrt{5} \cdot \sqrt{2^{2} \cdot 5}$

Step 5

Pull terms out from under the radical.

$16 \sqrt{5} \cdot (2 \sqrt{5})$

Step 6

Multiply $16 \sqrt{5} (2 \sqrt{5})$ .

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Step 6.1

Multiply $2$ by $16$ .

$32 \sqrt{5} \sqrt{5}$

Step 6.2

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

$32 ({\sqrt{5}}^{1} \sqrt{5})$

Step 6.3

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

$32 ({\sqrt{5}}^{1} {\sqrt{5}}^{1})$

Step 6.4

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

$32 {\sqrt{5}}^{1 + 1}$

Step 6.5

Add $1$ and $1$ .

$32 {\sqrt{5}}^{2}$

Step 7

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

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Step 7.1

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

$32 {(5^{\frac{1}{2}})}^{2}$

Step 7.2

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

$32 \cdot 5^{\frac{1}{2} \cdot 2}$

Step 7.3

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

$32 \cdot 5^{\frac{2}{2}}$

Step 7.4

Cancel the common factor of $2$ .

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Step 7.4.1

Cancel the common factor.

$32 \cdot 5^{\frac{2}{2}}$

Step 7.4.2

Rewrite the expression.

$32 \cdot 5^{1}$

Step 7.5

Evaluate the exponent.

$32 \cdot 5$

Step 8

Multiply $32$ by $5$ .

$160$