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How do you simplify $7 \div (5 - \sqrt{11})$ $7 div(5 - sqrt11)$ ?

1 Answer

Oct 21, 2015

$7 \div (5 - \sqrt{11}) = \frac{5 + \sqrt{11}}{2}$ $7 div (5-sqrt(11)) = (5+sqrt(11))/2$

Explanation:

$7 \div (5 - \sqrt{11}) = \frac{7}{5 - \sqrt{11}}$ $7div(5-sqrt(11)) = 7/(5-sqrt(11))$

rationalizing the denominator:
$XXX = \frac{7}{5 - \sqrt{11}} \cdot \frac{5 + \sqrt{11}}{5 + \sqrt{11}}$ $color(white)("XXX")= 7/(5-sqrt(11)) * (5+sqrt(11))/(5+sqrt(11))$

$XXX = \frac{7 (5 + \sqrt{11})}{25 - 11}$ $color(white)("XXX")=(7(5+sqrt(11)))/(25-11)$

$XXX = \frac{7 (5 + \sqrt{11})}{14}$ $color(white)("XXX")=(7(5+sqrt(11)))/14$

$XXX = \frac{5 + \sqrt{11}}{2}$ $color(white)("XXX")=(5+sqrt(11))/2$

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