Surds PS

Question

if x = 5 and y = 7

then root(x) + root(y) /( root( x + y ) = ?

12

root(5) + root(5)

root(15) + root(21) /( 6)

2

1

MHIKER · Answer

(√5+√7)/√(5+7)  
= (√5+√7)/√12
= (√5+√7)/2√3
=√3*(√5+√7)/2√3*√3
= (√15+√21)/6
Not sure.

gmat1220 · Answer

sqrt(5) = 2.2
sqrt(7) = 2.6
sqrt(12) = 3.3 (approx)

4.8/3.3 = 1.4

sqrt(15) = 4 (approx) --- close to 4.0
sqrt(21) = 4.6 (approx) --- close to 5.0

Option D becomes (4 + 4.6) / 6 = 8.6/6 = 1.4 (approx)

AnkitK · Answer

Dear gmat1220 ,Is it necessary to remember square root values in this ques?If yes ,which all square roots need to be memorized in context to GMAT?

beyondgmatscore · Answer

For this question kind, you dont really need to remember the roots. It is a simple rationalisation problem. Basically, you try and remove the roots from the denominator.

In this case, we want to find  (\sqrt{5}+\sqrt{7})/\sqrt{12}

Since the denominator is  \sqrt{12} , we multiply and divide the expression by  \sqrt{12}

We get (\sqrt{60}+\sqrt{84})/12

or  2/12*(\sqrt{15}+\sqrt{21})  which is the required answer

subhashghosh · Answer

Expression - {root(5) + root(7)}/root(12)

Multiply by root(3)/root(3)

= root(15) + root(21) /( 6)

Answer - D

MHIKER · Answer

subhashghosh, i did same thing that u did. thank u.

Banterninja · Answer

The Idea will be simplify the denominator first and make it a real number instead of a root. When that is done, we can simplify the roots in the numerator and obtain a new simplified fraction. I suppose it will help in looking at the answer choices to get an idea if you are lost.

Also, since the answer cannot be an integer, we can directly rule out couple of choices.

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