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

Redeem

Tricky OG 12 Question- need help

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
Newbie | Next Rank: 10 Posts
Posts: 5
Joined: Thu Jul 02, 2009 10:13 pm

Tricky OG 12 Question- need help

by JonDStewart » Fri Oct 02, 2009 2:45 pm
Question #117 in Problem Solving

117. If n is positive, which of the following is equal to 1/√ n+1 - √ n

so to clarify that is 1 divided by the square root of n plus one minus the square root of n.


now I multiplied by √ n+1 -√ n / √ n+1 -√ n

Basically I took the denominator and multiplied both the numerator and denominator by it.

and ended up with √ n+1 -√ n

Now when I checked the answer, I was close, but I was supposed to multiply by √ n+1 +√ n / √ n+1 +√ n
The difference is that it changed from minus the square root of n to plus the square root of n.

I was wondering how I am supposed to know to do this, and what rule this is.

the Answer is E) √ n+1 +√ n
Top
Source: — Problem Solving |
Newbie | Next Rank: 10 Posts
Posts: 5
Joined: Thu Jul 02, 2009 10:13 pm

by JonDStewart » Sat Oct 03, 2009 9:38 pm
Anyone? Please? I really would like to understand why the OG does this.

Thank you,
Top
Senior | Next Rank: 100 Posts
Posts: 34
Joined: Mon Aug 10, 2009 8:58 am
Thanked: 1 times

by mbadreams » Sun Oct 04, 2009 7:48 pm
When you have a root in the denominator, like 1/[√ x - √ y]. Then if you multiply numerator and denominator by the opposite sign of the denominator, then the root sign in the denominator will go by the formula.

1/[a-b] * [a + b]/[a + b] = a + b/ a^2 - b^2

I hope this is enough.
Top
Newbie | Next Rank: 10 Posts
Posts: 3
Joined: Mon Oct 12, 2009 5:43 pm
Location: University of Virginia
Thanked: 1 times

by YourDreamTheater » Mon Oct 12, 2009 10:07 pm
The goal when dealing with radicals is to square as many of the radicals as possible to make them "normal" (a.k.a. not under the square root sign).

So how can we make the denominator "normal" by getting rid of the radicals?
By squaring! Let's use the conjugate of the denominator

Think of it like a factoring problem --

Substitute w = sqrt(n+1) and j = sqrt(n)

Here's the denominator....
(w-j)(w+j) =(w^2 - j^2)=(n+1 - n) = 1


Bingo -- the denominator has been simplified.

Now both of the denominator's square roots have been squared and made "normal" again. Since we multiplied the denominator by w+j, we have to multiply the numerator by w+j, too.

As shown above, the denominator is equal to 1

we're left with w+j...

and that's choice E!


Whenever you have radicals in the denominator like this, try to multiply the denominator by its conjugate so the radicals square and cancel out.


Hope this helps!
Top
Post new topic Post Reply
• Page 1 of 1