Algebra Examples

$2 x^{2} \sqrt{5 x^{4}} + 7 \sqrt{5 x^{8}}$

Step 1

Simplify each term.

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Step 1.1

Rewrite $5 x^{4}$ as ${(x^{2})}^{2} \cdot 5$ .

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Step 1.1.1

Rewrite $x^{4}$ as ${(x^{2})}^{2}$ .

$2 x^{2} \sqrt{5 {(x^{2})}^{2}} + 7 \sqrt{5 x^{8}}$

Step 1.1.2

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

$2 x^{2} \sqrt{{(x^{2})}^{2} \cdot 5} + 7 \sqrt{5 x^{8}}$

Step 1.2

Pull terms out from under the radical.

$2 x^{2} (x^{2} \sqrt{5}) + 7 \sqrt{5 x^{8}}$

Step 1.3

Multiply $x^{2}$ by $x^{2}$ by adding the exponents.

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Step 1.3.1

Move $x^{2}$ .

$2 (x^{2} x^{2}) \sqrt{5} + 7 \sqrt{5 x^{8}}$

Step 1.3.2

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

$2 x^{2 + 2} \sqrt{5} + 7 \sqrt{5 x^{8}}$

Step 1.3.3

Add $2$ and $2$ .

$2 x^{4} \sqrt{5} + 7 \sqrt{5 x^{8}}$

Step 1.4

Rewrite $5 x^{8}$ as ${({(x^{2})}^{2})}^{2} \cdot 5$ .

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Step 1.4.1

Rewrite $x^{8}$ as ${(x^{4})}^{2}$ .

$2 x^{4} \sqrt{5} + 7 \sqrt{5 {(x^{4})}^{2}}$

Step 1.4.2

Reorder $5$ and ${(x^{4})}^{2}$ .

$2 x^{4} \sqrt{5} + 7 \sqrt{{(x^{4})}^{2} \cdot 5}$

Step 1.4.3

Rewrite $x^{4}$ as ${(x^{2})}^{2}$ .

$2 x^{4} \sqrt{5} + 7 \sqrt{{({(x^{2})}^{2})}^{2} \cdot 5}$

Step 1.5

Pull terms out from under the radical.

$2 x^{4} \sqrt{5} + 7 ({(x^{2})}^{2} \sqrt{5})$

Step 1.6

Multiply the exponents in ${(x^{2})}^{2}$ .

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Step 1.6.1

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

$2 x^{4} \sqrt{5} + 7 (x^{2 \cdot 2} \sqrt{5})$

Step 1.6.2

Multiply $2$ by $2$ .

$2 x^{4} \sqrt{5} + 7 (x^{4} \sqrt{5})$

$2 x^{4} \sqrt{5} + 7 x^{4} \sqrt{5}$

Step 2

Add $2 x^{4} \sqrt{5}$ and $7 x^{4} \sqrt{5}$ .

$9 x^{4} \sqrt{5}$