GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 22 Jan 2019, 05:43

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

## Events & Promotions

###### Events & Promotions in January
PrevNext
SuMoTuWeThFrSa
303112345
6789101112
13141516171819
20212223242526
272829303112
Open Detailed Calendar
• ### The winners of the GMAT game show

January 22, 2019

January 22, 2019

10:00 PM PST

11:00 PM PST

In case you didn’t notice, we recently held the 1st ever GMAT game show and it was awesome! See who won a full GMAT course, and register to the next one.
• ### Key Strategies to Master GMAT SC

January 26, 2019

January 26, 2019

07:00 AM PST

09:00 AM PST

Attend this webinar to learn how to leverage Meaning and Logic to solve the most challenging Sentence Correction Questions.

# Need Help- Addition and Subtraction under Square Roots

Author Message
TAGS:

### Hide Tags

Intern
Joined: 17 Dec 2016
Posts: 9
Location: United States (VA)
Schools: Kelley '21
GMAT 1: 450 Q21 V24
GPA: 3.81

### Show Tags

14 Apr 2018, 06:17
Hello

I am having difficulty with how to simplify addition and subtraction under a square root. Below is the problem and how it is stated in the Foundations of Math Manhattan Prep book. I also attached a copy of me trying to work out the problem. (AJ-WORK1 AND AJ-WORK2) The other attachment is the solution info that the book provides which isn't that clear to me. If someone can explain what I am doing wrong or how to look at this problem in a different way as well as some other examples perhaps ; that would be really great.

QUESTION #56 from Chapter 3 in FOM
Simplify the following root:Express expressions as integers

√(36^2 +15^2)

Felling super frustrated-AJ
Attachments

AJ-EXPLANTION-56.pdf [73.07 KiB]

AJ-WORK2.pdf [118.87 KiB]

AJ-WORK1.pdf [112.3 KiB]

Director
Joined: 30 Jan 2016
Posts: 889
Location: United States (MA)

### Show Tags

15 Apr 2018, 08:53
Hi Lnstnbass4,

I guess you made a mistake when you taking $$3^2$$ out.

$$\sqrt{36^2+15^2}$$=$$\sqrt{(2^2*3^2)^2+(3*5)^2}$$=$$\sqrt{2^4*3^4+3^2*5^2}$$=$$\sqrt{3^2(2^4*3^2+5^2)}$$=$$\sqrt{3^2(16*9+25)}$$=$$\sqrt{3^2(144+25)}$$=$$\sqrt{3^2*169}$$=$$\sqrt{3^2*13^2}$$=3*13=39

Hope this helps!
_________________

Non progredi est regredi

Manhattan Prep Instructor
Joined: 04 Dec 2015
Posts: 669
GMAT 1: 790 Q51 V49
GRE 1: Q170 V170

### Show Tags

20 Apr 2018, 12:40
Lnstnbass4 wrote:
Hello

I am having difficulty with how to simplify addition and subtraction under a square root. Below is the problem and how it is stated in the Foundations of Math Manhattan Prep book. I also attached a copy of me trying to work out the problem. (AJ-WORK1 AND AJ-WORK2) The other attachment is the solution info that the book provides which isn't that clear to me. If someone can explain what I am doing wrong or how to look at this problem in a different way as well as some other examples perhaps ; that would be really great.

QUESTION #56 from Chapter 3 in FOM
Simplify the following root:Express expressions as integers

√(36^2 +15^2)

Felling super frustrated-AJ

There's a quick way to solve this problem. (That's true on a lot of GMAT problems where the numbers seem too big to work with. They know you don't have a calculator, and they aren't really interested in testing your arithmetic skills beyond the basics, so if it looks like you might have to do a ton of arithmetic to solve a problem, there's probably another way to do it.)

Here's the right thought process for this problem.

1. There isn't really a math rule for adding together exponents, like 36^2 + 15^2.
2. However, there are two situations where you might see something like this on the test.
3. One is where you have two exponents with the same base added together, like 84^2 + 84^3. When you see this, factor out a common term. For instance, 84^2 + 84^3 = 84^2(1 + 84).
4. Another is where you're using the Pythagorean Theorem on a right triangle. That's a^2 + b^2 = c^2, or √(a^2 + b^2) = c.
5. Does this problem look like one of those two situations? It doesn't look like the first one, but it could look like the second one. Are 15 and 36 two sides of a right triangle?
6. A ratio of 15 to 36 is the same as a ratio of 15/3 to 36/3, or 5 to 12. There's a special right triangle that has sides with a ratio of 5 to 12! It's a (5,12,13) triangle.
7. Therefore, (5*3)^2 + (12*3)^2 = (13*3)^2.
8. Rephrasing that: sqrt(15^2 + 36^2) = sqrt(39^2) = 39.
_________________

Chelsey Cooley | Manhattan Prep | Seattle and Online

My latest GMAT blog posts | Suggestions for blog articles are always welcome!

Re: Need Help- Addition and Subtraction under Square Roots &nbs [#permalink] 20 Apr 2018, 12:40
Display posts from previous: Sort by