Algebra Examples

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

Step 1

Move $5$ to the left of $\sqrt{2}$ .

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

Step 2

Rewrite $8$ as $2^{2} \cdot 2$ .

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Step 2.1

Factor $4$ out of $8$ .

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

Step 2.2

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

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

Step 3

Pull terms out from under the radical.

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

Step 4

The absolute value is the distance between a number and zero. The distance between $0$ and $2$ is $2$ .

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

Step 5

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

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Step 5.1

Multiply $2$ by $5$ .

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

Step 5.2

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

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

Step 5.3

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

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

Step 5.4

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

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

Step 5.5

Add $1$ and $1$ .

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

Step 6

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

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Step 6.1

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

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

Step 6.2

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

$10 \cdot 2^{\frac{1}{2} \cdot 2}$

Step 6.3

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

$10 \cdot 2^{\frac{2}{2}}$

Step 6.4

Cancel the common factor of $2$ .

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Step 6.4.1

Cancel the common factor.

$10 \cdot 2^{\frac{2}{2}}$

Step 6.4.2

Rewrite the expression.

$10 \cdot 2^{1}$

Step 6.5

Evaluate the exponent.

$10 \cdot 2$

Step 7

Multiply $10$ by $2$ .

$20$