How do you simplify $2 \div (2 + \sqrt{2})$ $2div (2+sqrt(2))$ ?

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How do you simplify $2 \div (2 + \sqrt{2})$ $2div (2+sqrt(2))$ ?

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Answer 1 · 2018-05-06T07:59:22

$2 - \sqrt{2}$ $2-sqrt2$

Explanation:

$to simplify a fraction with a radical on the denominator$ $"to simplify a fraction with a radical on the denominator"$

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

$the conjugate of a \pm b is a \mp b$ $"the conjugate of "a+-b" is "acolor(red)(∓)b$

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

$\Rightarrow \frac{2}{2 + \sqrt{2}} \times \frac{2 - \sqrt{2}}{2 - \sqrt{2}}$ $rArr2/(2+sqrt2)xx(2-sqrt2)/(2-sqrt2)$

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

$= \frac{4 - 2 \sqrt{2}}{4 - 2} = \frac{4 - 2 \sqrt{2}}{2} = 2 - \sqrt{2}$ $=(4-2sqrt2)/(4-2)=(4-2sqrt2)/2=2-sqrt2$

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How do you simplify $2 \div (2 + \sqrt{2})$ $2div (2+sqrt(2))$ ?

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