How do you simplify $\frac{5 + \sqrt{5}}{8 - \sqrt{5}}$ $(5+ sqrt 5)/(8- sqrt 5)$ ?

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How do you simplify $\frac{5 + \sqrt{5}}{8 - \sqrt{5}}$ $(5+ sqrt 5)/(8- sqrt 5)$ ?

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Answer 1 · 2016-02-16T11:46:08

By multiply numerator and denominator by denominator's conjugate pair. Solution is $\frac{45 + 13 \sqrt 5}{59}$ $(45+13√5)/(59)$

Explanation:

To simplify $\frac{5 + \sqrt 5}{8 - \sqrt 5}$ $(5+√5)/(8−√5)$ , one has to multiply numerator and denominator by denominator's conjugate pair which is $(8 + \sqrt 5)$ $(8+√5)$ .

Hence, $\frac{5 + \sqrt 5}{8 - \sqrt 5}$ $(5+√5)/(8−√5)$ becomes

$\frac{(5 + \sqrt 5) (8 + \sqrt 5)}{(8 - \sqrt 5) (8 + \sqrt 5)}$ $((5+√5)(8+√5))/((8−√5)(8+√5))$ i.e.

$\frac{40 + 5 \sqrt 5 + 8 \sqrt 5 + 5}{64 - 5}$ $(40+5√5+8√5+5)/(64−5)$ i.e.

$\frac{45 + 13 \sqrt 5}{59}$ $(45+13√5)/(59)$

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How do you simplify $\frac{5 + \sqrt{5}}{8 - \sqrt{5}}$ $(5+ sqrt 5)/(8- sqrt 5)$ ?

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How do you simplify $\frac{5 + \sqrt{5}}{8 - \sqrt{5}}$ $(5+ sqrt 5)/(8- sqrt 5)$ ?