Which of the following is equivalent to √3+√2?

Question

A.  √5  
B.  \sqrt{5+2√6} 
C.  \sqrt{6+2√5}  
D.  \sqrt{5-2√6}  
E.  \sqrt{5+4√6}

0akshay0 · Accepted Answer

let x = √3+√2 ------------------I on squaring both sides, x^2 = (√3+√2)^2 x^2 = (√3)^2 + (√2)^2 + 2*(√3√2) x^2 = 3 + 2 + 2√6 x^2 = 5 + 2√6 taking square root on both sides x = \sqrt{5+2√6} √3+√2 = \sqrt{5+2√6} (from I) Hence option B is correct Hit Kudos if you liked it 8-)

origen87 · Answer

√3+√2=1.73+1.41=3.14

A quick look tells us that only B and C are close.
25^2=625. so sqrt(6) is approx 2.4; hence B=5+4.8=9.8
C=6+2*2.2>10.4

B is closer to our 3.14^2

MathRevolution · Answer

==> You get  √a+√b=\sqrt{a+b+2√ab}  because if you square both sides, you get  a+b+2\sqrt{ab}  on both sides. 
Thus, you get  √3+√2=\sqrt{5+2√6} .

The answer is B. Answer: B

BrentGMATPrepNow · Answer

KEY CONCEPT: If we take a positive number, square it and then take the square root of the result, we'll get back to the same number we started with. 
For example...
Take: 5
Square it to get: 25
Take the square root: √25
Evaluate: 5

Now let's answer the question: 
Take: √3+√2
Square it to get: (√3+√2)(√3+√2)
Use FOIL to expand : 3 + √6 + √6 + 2
Simplify: 5 + 2√6
Take the square root: √(5 + 2√6)

Answer: B

tsimo1000 · Answer

why the logic is not to square each number individually rather than collectively ? so, taking √3+√2, then squaring them individually will equal 3+2 = 5. then square root this to come with √5 , A.

Paras96 · Answer

Which of the following is equivalent to √3+√2?

Let √x = √3+√2
Squaring both sides,
=> x = 3 + 2 +2√6
=> x = 5+2√6

therefore, √x = √3+√2 = √(5+2√6)

hence B

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

Which of the following is equivalent to √3+√2?

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

Which of the following is equivalent to √3+√2?

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards