Is there a faster way to answer this GMAT question?

[SBronson]

There's gotta be a faster way to answer this question? Can anyone help?

117. If n is positive, which of the following is equal to:

1/(Rad (n+1)− Rad n)?
(A) 1
(B) Rad (2n+1)
(C) Rad (n+1)/Rad n
(D) Rad (n+1) − rad n
(E) Rad (n+1) + Rad n

The official guide explanation is about half a page long.

Thanks!

-Samantha

[GMATGuruNY]

Let n = 2.
Then:
1/(√n+1 - √n) = 1/(√3-√2) ≈ 1/(1.7 - 1.4) = 1/.3 = 10/3. This is our target.

Now plug n=2 into the answers to see which comes closest to our target of 10/3.

Only E works:
√(n+1) + √n = √3+√2 ≈ 1.7 + 1.4 = 3.1.

The correct answer is E.

[Raj700]

Nice! Thank you Mitch. That's so much easier. It certainly helps though to have rad 2 and rad 3 memorized.

-Raj

[Ashke]

1/(Rad (n+1)- Rad n)

= (Rad (n+1)+ Rad n)/((Rad (n+1)- Rad n))*(Rad (n+1)+ Rad n))

= (Rad (n+1)+ Rad n)

[fcabanski]

Here's an even faster answer:

"OnlyEworks"

Seriously, though, plugging in is often faster than working the algebra. But if you remember how to rationalize the denominator, as Ashke showed, the algebra on this one takes about 10 seconds.