BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

Roots in Division

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
Senior | Next Rank: 100 Posts
Posts: 66
Joined: Wed Sep 29, 2010 8:41 am
Location: Washhington, DC
Thanked: 8 times

Roots in Division

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.
Top
Source: — Problem Solving |
User avatar
Legendary Member
Posts: 1255
Joined: Fri Nov 07, 2008 2:08 pm
Location: St. Louis
Thanked: 312 times
Followed by:90 members

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
Top
Post new topic Post Reply
• Page 1 of 1