Rationalize the Numerator (4- square root of 7)/7

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

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

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

Combine.

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

Expand the numerator using the FOIL method.

$\frac{16 + 4 \sqrt{7} - 4 \sqrt{7} - {\sqrt{7}}^{2}}{7 (4 + \sqrt{7})}$

Simplify.

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

Apply the distributive property.

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

Multiply $7$ by $4$ .

$\frac{9}{28 + 7 \sqrt{7}}$

The result can be shown in multiple forms.

Exact Form:

$\frac{9}{28 + 7 \sqrt{7}}$

Decimal Form:

$0.19346409 \dots$

Rationalize the Numerator (4- square root of 7)/7

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