How do you simplify $\frac{3}{8 - \sqrt{2}}$ $3/ (8 - sqrt2)$ ?

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How do you simplify $\frac{3}{8 - \sqrt{2}}$ $3/ (8 - sqrt2)$ ?

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Answer 1 · 2016-04-02T08:01:08

$\frac{3}{8 - \sqrt{2}} = \frac{24 + 3 \sqrt{2}}{62}$ $3/(8-sqrt2)=(24+3sqrt2)/62$

Explanation:

From the given expression $\frac{3}{8 - \sqrt{2}}$ $3/(8-sqrt2)$ , start by rationalization by multiplying the expression by $\frac{8 + \sqrt{2}}{8 + \sqrt{2}}$ $(8+sqrt2)/(8+sqrt2)$

Let us do it

$\frac{3}{8 - \sqrt{2}} \cdot \frac{8 + \sqrt{2}}{8 + \sqrt{2}}$ $3/(8-sqrt2)*(8+sqrt2)/(8+sqrt2)$

$\frac{3 (8 + \sqrt{2})}{8^{2} - {(\sqrt{2})}^{2}}$ $(3(8+sqrt2))/(8^2-(sqrt2)^2)$

$\frac{24 + 3 \sqrt{2}}{64 - 2}$ $(24+3sqrt2)/(64-2)$

$\frac{24 + 3 \sqrt{2}}{62}$ $(24+3sqrt2)/62$

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How do you simplify $\frac{3}{8 - \sqrt{2}}$ $3/ (8 - sqrt2)$ ?

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