• The Princeton Review
    FREE GMAT Exam
    Know how you'd score today for $0

    Available with Beat the GMAT members only code

    MORE DETAILS
    The Princeton Review
  • Veritas Prep
    Free Veritas GMAT Class
    Experience Lesson 1 Live Free

    Available with Beat the GMAT members only code

    MORE DETAILS
    Veritas Prep
  • Economist Test Prep
    Free Trial & Practice Exam
    BEAT THE GMAT EXCLUSIVE

    Available with Beat the GMAT members only code

    MORE DETAILS
    Economist Test Prep
  • EMPOWERgmat Slider
    1 Hour Free
    BEAT THE GMAT EXCLUSIVE

    Available with Beat the GMAT members only code

    MORE DETAILS
    EMPOWERgmat Slider
  • Kaplan Test Prep
    Free Practice Test & Review
    How would you score if you took the GMAT

    Available with Beat the GMAT members only code

    MORE DETAILS
    Kaplan Test Prep
  • Magoosh
    Magoosh
    Study with Magoosh GMAT prep

    Available with Beat the GMAT members only code

    MORE DETAILS
    Magoosh
  • e-gmat Exclusive Offer
    Get 300+ Practice Questions
    25 Video lessons and 6 Webinars for FREE

    Available with Beat the GMAT members only code

    MORE DETAILS
    e-gmat Exclusive Offer
  • Target Test Prep
    5-Day Free Trial
    5-day free, full-access trial TTP Quant

    Available with Beat the GMAT members only code

    MORE DETAILS
    Target Test Prep
  • PrepScholar GMAT
    5 Day FREE Trial
    Study Smarter, Not Harder

    Available with Beat the GMAT members only code

    MORE DETAILS
    PrepScholar GMAT
  • Varsity Tutors
    Award-winning private GMAT tutoring
    Register now and save up to $200

    Available with Beat the GMAT members only code

    MORE DETAILS
    Varsity Tutors

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

This topic has 1 expert reply and 1 member reply

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

Post Thu Mar 01, 2018 6:47 am
Which of the following is equivalent to √3+√2? $$\left(A\right)\ \sqrt{5}$$ $$\left(B\right)\ \sqrt{5+2\sqrt{6}}$$ $$\left(C\right)\ \sqrt{6+2\sqrt{5}}$$ $$\left(D\right)\ \sqrt{5-2\sqrt{6}}$$ $$\left(E\right)\ \sqrt{5+4\sqrt{6}}$$ The Oa is the option B.

Experts, how can I rewrite the given expression to get one of the listed options? Can you show me the calculation needed?

  • +1 Upvote Post
  • Quote
  • Flag
Top Reply
Post Fri Mar 02, 2018 11:55 am
$$Take\ the\ square\ of\ \ \left(\sqrt{3}+\sqrt{2}\right)^2$$
$$\left(\sqrt{3}+\sqrt{2}\right)\left(\sqrt{3}+\sqrt{2}\right)=3+\sqrt{6}+\sqrt{6}+2$$
$$5+2\sqrt{6}$$
$$Take\ the\ square\ root\ of\ our\ result$$
$$we\ have\ \sqrt{5+2\sqrt{6}}$$
This correspond with option b

  • +1 Upvote Post
  • Quote
  • Flag

GMAT/MBA Expert

Post Thu Mar 01, 2018 9:51 am
M7MBA wrote:
Which of the following is equivalent to √3+√2? $$\left(A\right)\ \sqrt{5}$$ $$\left(B\right)\ \sqrt{5+2\sqrt{6}}$$ $$\left(C\right)\ \sqrt{6+2\sqrt{5}}$$ $$\left(D\right)\ \sqrt{5-2\sqrt{6}}$$ $$\left(E\right)\ \sqrt{5+4\sqrt{6}}$$
Nice question!

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

Cheers,
Brent

_________________
Brent Hanneson – Creator of GMATPrepNow.com
Use our video course along with Beat The GMAT's free 60-Day Study Guide

Check out the online reviews of our course
Come see all of our free resources

  • +1 Upvote Post
  • Quote
  • Flag
GMAT Prep Now's comprehensive video course can be used in conjunction with Beat The GMAT’s FREE 60-Day Study Guide and reach your target score in 2 months!

Top First Responders*

1 GMATGuruNY 103 first replies
2 Brent@GMATPrepNow 43 first replies
3 Rich.C@EMPOWERgma... 34 first replies
4 Jay@ManhattanReview 29 first replies
5 Scott@TargetTestPrep 11 first replies
* Only counts replies to topics started in last 30 days
See More Top Beat The GMAT Members

Most Active Experts

1 image description GMATGuruNY

The Princeton Review Teacher

152 posts
2 image description Brent@GMATPrepNow

GMAT Prep Now Teacher

139 posts
3 image description Scott@TargetTestPrep

Target Test Prep

104 posts
4 image description Max@Math Revolution

Math Revolution

86 posts
5 image description Rich.C@EMPOWERgma...

EMPOWERgmat

86 posts
See More Top Beat The GMAT Experts