How do you simplify sqrt5/(7-sqrt5)√57−√5?

2 Answers
sjc
May 16, 2018

1/44(5+7sqrt5)144(5+7√5)

Explanation:

sqrt5/(7-sqrt5)√57−√5

=sqrt5/(7-sqrt5)xx(7+sqrt5)/(7+sqrt5)=√57−√5×7+√57+√5

= (7sqrt5+5)/(49-5)=7√5+549−5

1/44(5+7sqrt5)144(5+7√5)

seol
May 16, 2018

(7\sqrt5+5)/547√5+554

Explanation:

\sqrt(5)/(7-\sqrt(5))√57−√5
To remove the square root in the denominator, multiply by its conjugate:
\sqrt(5)/(7-\sqrt(5))*(7+\sqrt(5))/(7+\sqrt(5))=(\sqrt(5)(7+\sqrt(5)))/((7-\sqrt(5))(7+\sqrt(5))√57−√5⋅7+√57+√5=√5(7+√5)(7−√5)(7+√5)

Now simplify that.
(7\sqrt5+5)/(49+\cancel(7\sqrt5-7\sqrt5)+5)
(7\sqrt5+5)/(49+5)=\color(tomato)((7\sqrt5+5)/54)

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