Algebra Examples

$\frac{\sqrt{2}}{\sqrt{72} + \sqrt{50} - \sqrt{8}}$

Step 1

Simplify the denominator.

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Step 1.1

Rewrite $72$ as $6^{2} \cdot 2$ .

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Step 1.1.1

Factor $36$ out of $72$ .

$\frac{\sqrt{2}}{\sqrt{36 (2)} + \sqrt{50} - \sqrt{8}}$

Step 1.1.2

Rewrite $36$ as $6^{2}$ .

$\frac{\sqrt{2}}{\sqrt{6^{2} \cdot 2} + \sqrt{50} - \sqrt{8}}$

Step 1.2

Pull terms out from under the radical.

$\frac{\sqrt{2}}{6 \sqrt{2} + \sqrt{50} - \sqrt{8}}$

Step 1.3

Rewrite $50$ as $5^{2} \cdot 2$ .

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Step 1.3.1

Factor $25$ out of $50$ .

$\frac{\sqrt{2}}{6 \sqrt{2} + \sqrt{25 (2)} - \sqrt{8}}$

Step 1.3.2

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

$\frac{\sqrt{2}}{6 \sqrt{2} + \sqrt{5^{2} \cdot 2} - \sqrt{8}}$

Step 1.4

Pull terms out from under the radical.

$\frac{\sqrt{2}}{6 \sqrt{2} + 5 \sqrt{2} - \sqrt{8}}$

Step 1.5

Rewrite $8$ as $2^{2} \cdot 2$ .

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Step 1.5.1

Factor $4$ out of $8$ .

$\frac{\sqrt{2}}{6 \sqrt{2} + 5 \sqrt{2} - \sqrt{4 (2)}}$

Step 1.5.2

Rewrite $4$ as $2^{2}$ .

$\frac{\sqrt{2}}{6 \sqrt{2} + 5 \sqrt{2} - \sqrt{2^{2} \cdot 2}}$

Step 1.6

Pull terms out from under the radical.

$\frac{\sqrt{2}}{6 \sqrt{2} + 5 \sqrt{2} - (2 \sqrt{2})}$

Step 1.7

Multiply $2$ by $- 1$ .

$\frac{\sqrt{2}}{6 \sqrt{2} + 5 \sqrt{2} - 2 \sqrt{2}}$

Step 1.8

Add $6 \sqrt{2}$ and $5 \sqrt{2}$ .

$\frac{\sqrt{2}}{11 \sqrt{2} - 2 \sqrt{2}}$

Step 1.9

Subtract $2 \sqrt{2}$ from $11 \sqrt{2}$ .

$\frac{\sqrt{2}}{9 \sqrt{2}}$

Step 2

Cancel the common factor of $\sqrt{2}$ .

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Step 2.1

Cancel the common factor.

$\frac{\sqrt{2}}{9 \sqrt{2}}$

Step 2.2

Rewrite the expression.

$\frac{1}{9}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{9}$

Decimal Form:

$0.\overline{1}$