Algebra Examples

$\frac{9}{\sqrt{5} + \sqrt{2}}$

Step 1

Multiply $\frac{9}{\sqrt{5} + \sqrt{2}}$ by $\frac{\sqrt{5} - \sqrt{2}}{\sqrt{5} - \sqrt{2}}$ .

$\frac{9}{\sqrt{5} + \sqrt{2}} \cdot \frac{\sqrt{5} - \sqrt{2}}{\sqrt{5} - \sqrt{2}}$

Step 2

Multiply $\frac{9}{\sqrt{5} + \sqrt{2}}$ by $\frac{\sqrt{5} - \sqrt{2}}{\sqrt{5} - \sqrt{2}}$ .

$\frac{9 (\sqrt{5} - \sqrt{2})}{(\sqrt{5} + \sqrt{2}) (\sqrt{5} - \sqrt{2})}$

Step 3

Expand the denominator using the FOIL method.

$\frac{9 (\sqrt{5} - \sqrt{2})}{{\sqrt{5}}^{2} - \sqrt{10} + \sqrt{10} - {\sqrt{2}}^{2}}$

Step 4

Simplify.

$\frac{9 (\sqrt{5} - \sqrt{2})}{3}$

Step 5

Cancel the common factor of $9$ and $3$ .

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Step 5.1

Factor $3$ out of $9 (\sqrt{5} - \sqrt{2})$ .

$\frac{3 (3 (\sqrt{5} - \sqrt{2}))}{3}$

Step 5.2

Cancel the common factors.

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Step 5.2.1

Factor $3$ out of $3$ .

$\frac{3 (3 (\sqrt{5} - \sqrt{2}))}{3 (1)}$

Step 5.2.2

Cancel the common factor.

$\frac{3 (3 (\sqrt{5} - \sqrt{2}))}{3 \cdot 1}$

Step 5.2.3

Rewrite the expression.

$\frac{3 (\sqrt{5} - \sqrt{2})}{1}$

Step 5.2.4

Divide $3 (\sqrt{5} - \sqrt{2})$ by $1$ .

$3 (\sqrt{5} - \sqrt{2})$

Step 6

Apply the distributive property.

$3 \sqrt{5} + 3 (- \sqrt{2})$

Step 7

Multiply $- 1$ by $3$ .

$3 \sqrt{5} - 3 \sqrt{2}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$3 \sqrt{5} - 3 \sqrt{2}$

Decimal Form:

$2.46556324 \dots$