How do you rationalize the denominator and simplify $(3sqrt2 + 2sqrt7)/( sqrt7 - 5sqrt2)$ ?

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Answer 1 · 2018-03-23T21:17:03

$-(44+13sqrt(14))/43$

We first multiply the numerator and the denominator of this fraction by the conjugate of the denominator.

The denominator is $sqrt(7)-5sqrt(2)$ , so its conjugate is $sqrt(7)+5sqrt(2)$ , Let's do the multiplication.

$(3sqrt(2)+2sqrt(7))/(sqrt(7)-5sqrt(2))*(sqrt(7)+5sqrt(2))/(sqrt(7)+5sqrt(2))$

$((3sqrt(2)+2sqrt(7))(sqrt(7)+5sqrt(2)))/((sqrt(7)-5sqrt(2))(sqrt(7)+5sqrt(2)))$

$(3sqrt(14)+15*2+2*7+10sqrt(14))/(7+5sqrt(14)-5sqrt(14)-25*2)$

Simplifying we have

$(44+13sqrt(14))/(-43)=-(44+13sqrt(14))/43$ .

How do you rationalize the denominator and simplify (3sqrt2 + 2sqrt7)/( sqrt7 - 5sqrt2)(3sqrt2 + 2sqrt7)/( sqrt7 - 5sqrt2)?