• 7 CATs FREE!
    If you earn 100 Forum Points

    Engage in the Beat The GMAT forums to earn
    100 points for $49 worth of Veritas practice GMATs FREE

    Veritas Prep
    VERITAS PRACTICE GMAT EXAMS
    Earn 10 Points Per Post
    Earn 10 Points Per Thanks
    Earn 10 Points Per Upvote
    REDEEM NOW

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
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
$$Take\ the\ square\ of\ \ \left(\sqrt{3}+\sqrt{2}\right)^2$$
$$\left(\sqrt{3}+\sqrt{2}\right)\left(\sqrt{3}+\sqrt{2}\right)=3+\sqrt{6}+\sqrt{6}+2$$
$$5+2\sqrt{6}$$
$$Take\ the\ square\ root\ of\ our\ result$$
$$we\ have\ \sqrt{5+2\sqrt{6}}$$
This correspond with option b

  • +1 Upvote Post
  • Quote
  • Flag

GMAT/MBA Expert

Post
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

Sign up for our free Question of the Day emails
And check out 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!
  • Veritas Prep
    Free Veritas GMAT Class
    Experience Lesson 1 Live Free

    Available with Beat the GMAT members only code

    MORE DETAILS
    Veritas Prep
  • 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
  • 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
  • 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
  • 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
  • Magoosh
    Magoosh
    Study with Magoosh GMAT prep

    Available with Beat the GMAT members only code

    MORE DETAILS
    Magoosh
  • EMPOWERgmat Slider
    1 Hour Free
    BEAT THE GMAT EXCLUSIVE

    Available with Beat the GMAT members only code

    MORE DETAILS
    EMPOWERgmat Slider
  • PrepScholar GMAT
    5 Day FREE Trial
    Study Smarter, Not Harder

    Available with Beat the GMAT members only code

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

    Available with Beat the GMAT members only code

    MORE DETAILS
    Economist Test Prep
  • 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

Top First Responders*

1 Brent@GMATPrepNow 69 first replies
2 fskilnik@GMATH 54 first replies
3 Jay@ManhattanReview 48 first replies
4 GMATGuruNY 35 first replies
5 Rich.C@EMPOWERgma... 31 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 fskilnik@GMATH

GMATH Teacher

128 posts
2 image description Brent@GMATPrepNow

GMAT Prep Now Teacher

101 posts
3 image description Max@Math Revolution

Math Revolution

92 posts
4 image description Jay@ManhattanReview

Manhattan Review

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

EMPOWERgmat

78 posts
See More Top Beat The GMAT Experts