Algebra Examples

$\sqrt{2} (3 \sqrt{2} + 2 \sqrt{2})$

Step 1

Add $3 \sqrt{2}$ and $2 \sqrt{2}$ .

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

Step 2

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

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Step 2.1

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

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

Step 2.2

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

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

Step 2.3

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

$5 {\sqrt{2}}^{1 + 1}$

Step 2.4

Add $1$ and $1$ .

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

Step 3

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

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Step 3.1

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

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

Step 3.2

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

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

Step 3.3

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

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

Step 3.4

Cancel the common factor of $2$ .

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Step 3.4.1

Cancel the common factor.

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

Step 3.4.2

Rewrite the expression.

$5 \cdot 2^{1}$

Step 3.5

Evaluate the exponent.

$5 \cdot 2$

Step 4

Multiply $5$ by $2$ .

$10$