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

Redeem

Arithmetic

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
Moderator
Posts: 772
Joined: Wed Aug 30, 2017 6:29 pm
Followed by:6 members

Arithmetic

by BTGmoderatorRO » Sat Nov 11, 2017 8:25 am
If the sum of the square roots of two integers is $$\sqrt{9+6+\sqrt{2}}$$ , what is the sum of the squares of these two integers?

(A) 40
(B) 43
(C) 45
(D) 48
(E) 52

OA is c.

Can any Expert help me out on how to solve this question correctly? i will gladly appreciate your contribution. Thanks
Top
Source: — Problem Solving |

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 16207
Joined: Mon Dec 08, 2008 6:26 pm
Location: Vancouver, BC
Thanked: 5254 times
Followed by:1268 members
GMAT Score:770

by Brent@GMATPrepNow » Mon Nov 13, 2017 1:57 pm
Roland2rule wrote:If the sum of the square roots of two integers is $$\sqrt{9+6+\sqrt{2}}$$ , what is the sum of the squares of these two integers?

(A) 40
(B) 43
(C) 45
(D) 48
(E) 52

OA is c.

Can any Expert help me out on how to solve this question correctly? i will gladly appreciate your contribution. Thanks
Are you sure you transcribed the question correctly?

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
Image
Top

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 8089
Joined: Sat Apr 25, 2015 10:56 am
Location: Los Angeles, CA
Thanked: 43 times
Followed by:29 members

by Scott@TargetTestPrep » Tue Jan 09, 2018 10:14 am
Roland2rule wrote:If the sum of the square roots of two integers is $$\sqrt{9+6+\sqrt{2}}$$ , what is the sum of the squares of these two integers?

(A) 40
(B) 43
(C) 45
(D) 48
(E) 52
We can let a = the first integer and b = the second integer. Thus:

√a + √b = √(9 + 6√2)

We are asked to find a^2 + b^2.

Let's square both sides of the equation above.

(√a + √b)^2 = [√(9 + 6√2)]^2

a + 2√ab + b = 9 + 6√2

Since a and b are integers, we must have:

a + b = 9 and 2√ab = 6√2

If we square both sides of a + b = 9, we have:

a^2 + 2ab + b^2 = 81

If we square both sides of 2√ab = 6√2, we have:

4ab = 36(2)

2ab = 36

We can now substitute 36 for 2ab in a^2 + 2ab + b^2 = 81 to obtain:

a^2 + 36 + b^2 = 81

a^2 + b^2 = 45

Answer: C

Scott Woodbury-Stewart
Founder and CEO
[email protected]

Image

See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews

ImageImage
Top

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 8089
Joined: Sat Apr 25, 2015 10:56 am
Location: Los Angeles, CA
Thanked: 43 times
Followed by:29 members

by Scott@TargetTestPrep » Tue Jan 09, 2018 10:15 am
Scott@TargetTestPrep wrote:
Roland2rule wrote:If the sum of the square roots of two integers is $$\sqrt{9+6\sqrt{2}}$$ , what is the sum of the squares of these two integers?

(A) 40
(B) 43
(C) 45
(D) 48
(E) 52
The correct version of this problem is above.

We can let a = the first integer and b = the second integer. Thus:

√a + √b = √(9 + 6√2)

We are asked to find a^2 + b^2.

Let's square both sides of the equation above.

(√a + √b)^2 = [√(9 + 6√2)]^2

a + 2√ab + b = 9 + 6√2

Since a and b are integers, we must have:

a + b = 9 and 2√ab = 6√2

If we square both sides of a + b = 9, we have:

a^2 + 2ab + b^2 = 81

If we square both sides of 2√ab = 6√2, we have:

4ab = 36(2)

2ab = 36

We can now substitute 36 for 2ab in a^2 + 2ab + b^2 = 81 to obtain:

a^2 + 36 + b^2 = 81

a^2 + b^2 = 45

Answer: C
Top
Post new topic Post Reply
• Page 1 of 1