Algebra Examples

$\frac{14}{3 + \sqrt{2}}$

Step 1

Multiply $\frac{14}{3 + \sqrt{2}}$ by $\frac{3 - \sqrt{2}}{3 - \sqrt{2}}$ .

$\frac{14}{3 + \sqrt{2}} \cdot \frac{3 - \sqrt{2}}{3 - \sqrt{2}}$

Step 2

Multiply $\frac{14}{3 + \sqrt{2}}$ by $\frac{3 - \sqrt{2}}{3 - \sqrt{2}}$ .

$\frac{14 (3 - \sqrt{2})}{(3 + \sqrt{2}) (3 - \sqrt{2})}$

Step 3

Expand the denominator using the FOIL method.

$\frac{14 (3 - \sqrt{2})}{9 - 3 \sqrt{2} + \sqrt{2} \cdot 3 - {\sqrt{2}}^{2}}$

Step 4

Simplify.

$\frac{14 (3 - \sqrt{2})}{7}$

Step 5

Cancel the common factor of $14$ and $7$ .

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Step 5.1

Factor $7$ out of $14 (3 - \sqrt{2})$ .

$\frac{7 (2 (3 - \sqrt{2}))}{7}$

Step 5.2

Cancel the common factors.

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Step 5.2.1

Factor $7$ out of $7$ .

$\frac{7 (2 (3 - \sqrt{2}))}{7 (1)}$

Step 5.2.2

Cancel the common factor.

$\frac{7 (2 (3 - \sqrt{2}))}{7 \cdot 1}$

Step 5.2.3

Rewrite the expression.

$\frac{2 (3 - \sqrt{2})}{1}$

Step 5.2.4

Divide $2 (3 - \sqrt{2})$ by $1$ .

$2 (3 - \sqrt{2})$

Step 6

Apply the distributive property.

$2 \cdot 3 + 2 (- \sqrt{2})$

Step 7

Multiply.

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Step 7.1

Multiply $2$ by $3$ .

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

Step 7.2

Multiply $- 1$ by $2$ .

$6 - 2 \sqrt{2}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$6 - 2 \sqrt{2}$

Decimal Form:

$3.17157287 \dots$