BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

Target Test Prep · GMAT

Choose how you want to prepare

Learn live with an expert or move at your own pace. Every option includes the complete TTP study system.

★★★★★5.0559 reviews
GMATBootcamp Starts Sep 21
Chris Peckover, Target Test Prep GMAT expert
LIVE ONLINE BOOTCAMP

Live Online Bootcamp Class with Top GMAT Expert Chris Peckover

Sep 21 to Oct 9, 2026

Schedule
Mon to Fri · 7:00 to 10:00 PM ET
Included
Live classes + 6 months of TTP OnDemand
  • Boost your GMAT score in less than one month in a live online class
  • 6 months access to TTP OnDemand video courses included
View bootcamp & enroll
Limited cohort · enrollment openTarget Test Prep
EALiveTeach 5 seats left
Logan Thompson
EXECUTIVE ASSESSMENT

Sep 6 to Dec 6, 2026

with Logan Thompson

Schedule
Sun · 9:30 AM to 12:30 PM ET
Included
40 hours of live online classes plus six months of access to the complete TTP EA OnDemand course.
  • 165+ EA Score Guarantee
  • 4,100+ Quant, Verbal, and Integrated Reasoning practice questions
  • 400+ hours of in-depth video lessons
  • 3,000+ step-by-step video solutions
View EA class & enroll
Limited cohort · enrollment openTarget Test Prep
GMATOnDemand Start anytime
SELF-PACED MASTERCLASS

Target Test Prep GMAT OnDemand

Complete access from day one. Study on your schedule.

715+ score guarantee
$0to start then $127/mo
  • Personalized study plan and analytics
  • Thousands of lessons and practice questions
Start free 5-day trial
Read 559 reviewsTarget Test Prep

Compare the format, schedule, and included access before enrolling. Prices and seat counts shown reflect the supplied offer details.

3 prep questions on square root equations

Expert replies
Post new topic Post Reply
Previous Topic Next Topic
Senior | Next Rank: 100 Posts
Posts: 48
Joined: Sat Nov 28, 2009 1:01 pmFollowed by: 1 member
Thanked: 1 times
by Mr_T » Tue Jan 19, 2010 2:24 pm
Hi everyone,

I seem to have some problems with some equations containing the root of something. It would be great if someone took a look.

1) if M = 4^1/2 + 4^1/3 + 4^1/4, then the value of M is...
a) Less than 3
b) Equal to 3
c) between 3 and 4
d) equal to 4
e) greater than 4 -> Ans, but how? by approx.?

2) If x and y are positive, which of the following must be greater than 1 / (x+y)^1/2

I. (x+y)^1/2 / 2x
II. (x^1/2 + y^1/2) / x+y
III. (x^1/2 - y^1/2) / x+y

3) Loss the question but I think it was: Solve ( ((9+80^1/2)^1/2 + (9-80^1/2)^1/2)^2


Thanks,

mr T
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Source: — Problem Solving |
Senior | Next Rank: 100 Posts
Posts: 98
Joined: Mon Nov 23, 2009 2:30 pmFollowed by: 1 member
Thanked: 26 times

by ace_gre » Tue Jan 19, 2010 4:04 pm
Hi, Here is my approach..

1. M = 4^1/2 + 4^1/3 + 4^1/4
M = 4 ^6/12 + 4^ 4/12 + 4^3/12
M = 4^(3/12) *( 4^2+ 4^1 + 1)
M = 4^1/4*(21)
M=2^1/2 * 21
M ~1.414*21 and is greater than 4.

2. Lets say x=1,y=1,
1/(x+y)^1/2 = 1/ 2^1/2

I. 2^1/2 / 2 ==> 1/ 2^1/2 which is equal. Hence not true.

II. x=1,y=1
1/(x+y)^1/2 = 1/ 2^1/2 ==>(2)^1/2
(x^1/2 + y^1/2) / x+y ==> 1. true.
Check for fractions. lets say x= 1/4 and y=1/4.
exp II is greater

III. (x^1/2 - y^1/2) / x+y
when x=1, y=1, II becomes 0. Hence not greater.

IMO II is true.

3. Based on the question, I say let a = 9, b= 80^1/2
exp = ((a+b) ^1/2 + (a-b)^ 1/2 )^2
==> a+b +a-b +2 (a+b)^1/2 (a-b) ^1/2
==>2a +2(a^2 - b^2)^1/2
==>2(9) + 2( 81 - 80) ^1/2
==>20.

IMO 20
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Senior | Next Rank: 100 Posts
Posts: 48
Joined: Sat Nov 28, 2009 1:01 pmFollowed by: 1 member
Thanked: 1 times

by Mr_T » Tue Jan 19, 2010 7:08 pm
Thanks!

Actually, you made a mistake in the first problem when you tried to factor out 4^3/12. It's ok I figured out how to approximate the answer. For question 2, I wanted to see if there was a way to simplify the equations instead of plugging numbers. Your answer for the third one is dead on. I should have seen that the exponents were the same so I could multiply their base...

Thanks again.

mr T
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Newbie | Next Rank: 10 Posts
Posts: 5
Joined: Tue Jan 05, 2010 11:02 am
Thanked: 1 times

by nicolas » Sun Jan 31, 2010 1:01 am
ace_gre wrote:Hi, Here is my approach..

1. M = 4^1/2 + 4^1/3 + 4^1/4
M = 4 ^6/12 + 4^ 4/12 + 4^3/12
M = 4^(3/12) *( 4^2+ 4^1 + 1)
M = 4^1/4*(21)
M=2^1/2 * 21
M ~1.414*21 and is greater than 4.
Hi ace_gre,

actually you got a flaw in your calculation:
M = 4 ^6/12 + 4^ 4/12 + 4^3/12 is not equal to M = 4^(3/12) *( 4^2+ 4^1 + 1), as you multiplied the exponents, although you have to add them.
If you want to factor out the right equation would be:
M = 4 ^6/12 + 4^ 4/12 + 4^3/12
M = 4 ^3/12 *(4 ^3/12 + 4^1/12 + 1)
..
I would find another method beneficial, namely:
Take a look:
4^1/2 + 4^1/3 + 4^1/4

--> The first term 4^1/2 = 2
--> The second term is 4^1/3, we don't know what that is, but it states that x*x*x = 4, i.e. at least x>1 has to be true!
--> The third term is 4^1/4 = (2^2)^1/4 = 2^1/2, i.e. the square root of 2, which is something about 1.4, i.e. >1

So we have 2 + >1 + >1 and that is at least > 4!

Thus E
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Post new topic Post Reply
• Page 1 of 1