Pre-Algebra Examples

$- 9 x^{4} \sqrt{5} - 11 \sqrt{125 x^{8}}$

Step 1

Simplify each term.

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Step 1.1

Rewrite $125 x^{8}$ as ${(5 x^{4})}^{2} \cdot 5$ .

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Step 1.1.1

Factor $25$ out of $125$ .

$- 9 x^{4} \sqrt{5} - 11 \sqrt{25 (5) x^{8}}$

Step 1.1.2

Rewrite $25$ as $5^{2}$ .

$- 9 x^{4} \sqrt{5} - 11 \sqrt{5^{2} \cdot 5 x^{8}}$

Step 1.1.3

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

$- 9 x^{4} \sqrt{5} - 11 \sqrt{5^{2} \cdot 5 {(x^{4})}^{2}}$

Step 1.1.4

Move $5$ .

$- 9 x^{4} \sqrt{5} - 11 \sqrt{5^{2} {(x^{4})}^{2} \cdot 5}$

Step 1.1.5

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

$- 9 x^{4} \sqrt{5} - 11 \sqrt{{(5 x^{4})}^{2} \cdot 5}$

Step 1.2

Pull terms out from under the radical.

$- 9 x^{4} \sqrt{5} - 11 (5 x^{4} \sqrt{5})$

Step 1.3

Multiply $5$ by $- 11$ .

$- 9 x^{4} \sqrt{5} - 55 x^{4} \sqrt{5}$

Step 2

Subtract $55 x^{4} \sqrt{5}$ from $- 9 x^{4} \sqrt{5}$ .

$- 64 x^{4} \sqrt{5}$