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Notice that the expression under the square root sign is of the form (x-y)(x+y). And recall that (x+y)(x-y)=x2-y2. This is another one of the GMAT’s favorite expressions.

Returning to our expression:

2(V((24+5V23)*(24-5V23))= 2V(242-(5V23) 2)=2V(242-25*23)=2V(576-575)=2V1=2.

Finally then: x2+y2+2xy=48+2=50.

But now we must remember to “unsquare” (or take the square root of) our answer: V50=V(25*2)=5V2.

Therefore, the correct answer is D.

Resume:

To solve problems with roots it is useful to remember algebraic expressions and formulas. Using them in time will help you to make hard problem much easier.

Material prepared by Ksenia Zueva

GMAT consultant at МВА Strategy

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