Rationalize the Denominator 4/(9- square root of 7)

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$\frac{4}{9 - \sqrt{7}}$

Multiply $\frac{4}{9 - \sqrt{7}}$ by $\frac{9 + \sqrt{7}}{9 + \sqrt{7}}$ .

$\frac{4}{9 - \sqrt{7}} \cdot \frac{9 + \sqrt{7}}{9 + \sqrt{7}}$

Multiply $\frac{4}{9 - \sqrt{7}}$ and $\frac{9 + \sqrt{7}}{9 + \sqrt{7}}$ .

$\frac{4 (9 + \sqrt{7})}{(9 - \sqrt{7}) (9 + \sqrt{7})}$

Expand the denominator using the FOIL method.

$\frac{4 (9 + \sqrt{7})}{81 + 9 \sqrt{7} - 9 \sqrt{7} - {\sqrt{7}}^{2}}$

Simplify.

$\frac{4 (9 + \sqrt{7})}{74}$

Cancel the common factor of $4$ and $74$ .

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Factor $2$ out of $4 (9 + \sqrt{7})$ .

$\frac{2 (2 (9 + \sqrt{7}))}{74}$

Cancel the common factors.

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Factor $2$ out of $74$ .

$\frac{2 (2 (9 + \sqrt{7}))}{2 (37)}$

Cancel the common factor.

$\frac{2 (2 (9 + \sqrt{7}))}{2 \cdot 37}$

Rewrite the expression.

$\frac{2 (9 + \sqrt{7})}{37}$

The result can be shown in multiple forms.

Exact Form:

$\frac{2 (9 + \sqrt{7})}{37}$

Decimal Form:

$0.62950007 \dots$

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