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Roots in Division

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by jk2010 » Sat Mar 05, 2011 11:10 am
Sqrt 5 + 2 / Sqrt 5 -2

A) 4
B) Sqrt 5+2
C) 9
D) 9 + 4 Sqrt 5
E) 25

Answer d

This question is from one of the 800 Score CATs. I don't quite follow their explanation which focuses on turning the denominator into a 1. I know there is a simple way to do this, but I am drawing a blank.

Thanks.
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by Tani » Sat Mar 05, 2011 12:03 pm
They are using the "difference of two squares" to simplify the denominator.

(x+y)*(x-y) = x^2 - y^2.

If you multiply the fraction by (Sqrt 5 + 2)/(Sqrt 5 + 2), you will not change the value of the expression since your multiplier equals 1.

The bottom, however, is now (Sqrt 5 -2) * (Sqrt 5 + 2) . You have an (x+y)*(x-y) situation and the product is

(Sqrt5)^2 - 2^2 = 5 - 4 = 1.

Then you simply FOIL the top and get 5 + 4(Sqrt5) + 4 or 9 + 4(Sqrt5)
Tani Wolff
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