What is $(sqrt7- 5)/(sqrt2 + 5 )$ ?

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Answer 1 · 2015-06-12T19:21:29

The answer is $-(sqrt14-5sqrt7-5sqrt2+25)/(23)$ .

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

Rationalize the denominator by multiplying the numerator and denominator by $(sqrt2-5)$ .

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

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

The denominator is in the form of the difference of squares: $a^2-b^2$

$((sqrt 7-5)(sqrt 2-5))/((sqrt2)^2-5^2)$ =

$((sqrt 7-5)(sqrt 2-5))/(2-25)$ =

$((sqrt 7-5)(sqrt 2-5))/(-23)$

FOIL the numerator.

$(sqrt14-5sqrt7-5sqrt2+25)/(-23)$ =

$-(sqrt14-5sqrt7-5sqrt2+25)/(23)$

What is (sqrt7- 5)/(sqrt2 + 5 )(sqrt7- 5)/(sqrt2 + 5 )?