Algebra Examples

$\frac{\sqrt{8}}{\sqrt{100}}$

Step 1

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

$\sqrt{\frac{8}{100}}$

Step 2

Cancel the common factor of $8$ and $100$ .

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Step 2.1

Factor $4$ out of $8$ .

$\sqrt{\frac{4 (2)}{100}}$

Step 2.2

Cancel the common factors.

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Step 2.2.1

Factor $4$ out of $100$ .

$\sqrt{\frac{4 \cdot 2}{4 \cdot 25}}$

Step 2.2.2

Cancel the common factor.

$\sqrt{\frac{4 \cdot 2}{4 \cdot 25}}$

Step 2.2.3

Rewrite the expression.

$\sqrt{\frac{2}{25}}$

Step 3

Rewrite $\sqrt{\frac{2}{25}}$ as $\frac{\sqrt{2}}{\sqrt{25}}$ .

$\frac{\sqrt{2}}{\sqrt{25}}$

Step 4

Simplify the denominator.

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Step 4.1

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

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

Step 4.2

Pull terms out from under the radical.

$\frac{\sqrt{2}}{| 5 |}$

Step 4.3

The absolute value is the distance between a number and zero. The distance between $0$ and $5$ is $5$ .

$\frac{\sqrt{2}}{5}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{\sqrt{2}}{5}$

Decimal Form:

$0.28284271 \dots$