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

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

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Answer 1 · 2018-06-17T10:27:33

$\frac{1}{7} (24 - 8 \sqrt{2})$ $1/7(24-8sqrt2)$

Explanation:

$multiply the numerator/denominator by the conjugate$ $"multiply the numerator/denominator by the "color(blue)"conjugate"$
$of the denominator$ $"of the denominator"$

$the conjugate of 3 + \sqrt{2} is 3 - \sqrt{2}$ $"the conjugate of "3+sqrt2" is "3color(red)(-)sqrt2$

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

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

$= \frac{24 - 8 \sqrt{2}}{7} = \frac{1}{7} (24 - 8 \sqrt{2})$ $=(24-8sqrt2)/7=1/7(24-8sqrt2)$

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

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