Algebra Examples

$\frac{\sqrt{100 a^{8}}}{\sqrt{25 a^{4}}}$

Step 1

Combine $\sqrt{100 a^{8}}$ and $\sqrt{25 a^{4}}$ into a single radical.

$\sqrt{\frac{100 a^{8}}{25 a^{4}}}$

Step 2

Reduce the expression $\frac{100 a^{8}}{25 a^{4}}$ by cancelling the common factors.

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Step 2.1

Factor $25$ out of $100 a^{8}$ .

$\sqrt{\frac{25 (4 a^{8})}{25 a^{4}}}$

Step 2.2

Factor $25$ out of $25 a^{4}$ .

$\sqrt{\frac{25 (4 a^{8})}{25 (a^{4})}}$

Step 2.3

Cancel the common factor.

$\sqrt{\frac{25 (4 a^{8})}{25 a^{4}}}$

Step 2.4

Rewrite the expression.

$\sqrt{\frac{4 a^{8}}{a^{4}}}$

Step 3

Cancel the common factor of $a^{8}$ and $a^{4}$ .

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Step 3.1

Factor $a^{4}$ out of $4 a^{8}$ .

$\sqrt{\frac{a^{4} (4 a^{4})}{a^{4}}}$

Step 3.2

Cancel the common factors.

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Step 3.2.1

Multiply by $1$ .

$\sqrt{\frac{a^{4} (4 a^{4})}{a^{4} \cdot 1}}$

Step 3.2.2

Cancel the common factor.

$\sqrt{\frac{a^{4} (4 a^{4})}{a^{4} \cdot 1}}$

Step 3.2.3

Rewrite the expression.

$\sqrt{\frac{4 a^{4}}{1}}$

Step 3.2.4

Divide $4 a^{4}$ by $1$ .

$\sqrt{4 a^{4}}$

Step 4

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

$\sqrt{{(2 a^{2})}^{2}}$

Step 5

Pull terms out from under the radical.

$| 2 a^{2} |$

Step 6

Remove non-negative terms from the absolute value.

$2 a^{2}$