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Math Expert V
Joined: 02 Sep 2009
Posts: 58402

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3 00:00

Difficulty:   5% (low)

Question Stats: 87% (00:49) correct 13% (01:10) wrong based on 142 sessions

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$$\sqrt{324} + \sqrt{289} = ?$$

A. 32
B. 33
C. 34
D. 35
E. 36

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Math Expert V
Joined: 02 Sep 2009
Posts: 58402

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Official Solution:

$$\sqrt{324} + \sqrt{289} = ?$$

A. 32
B. 33
C. 34
D. 35
E. 36

$$\sqrt{324} = 18$$; $$\sqrt{289} = 17$$; $$18 + 17 = 35$$.

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I can get to 324 = 2^2 * 3^4 easily by decomposing the number, but not 289 because it's a prime number. So how am i supposed to know that 289 is 17 squared? How many number squares am I supposed to remember for the gmat?
Intern  Joined: 13 Nov 2013
Posts: 23
Location: Brazil
Concentration: Strategy, Marketing
GMAT 1: 640 Q44 V35 GMAT 2: 690 Q48 V36 Show Tags

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pietropietro wrote:
I can get to 324 = 2^2 * 3^4 easily by decomposing the number, but not 289 because it's a prime number. So how am i supposed to know that 289 is 17 squared? How many number squares am I supposed to remember for the gmat?

I share your thoughts, the last part was harder for me too. But looking at 289 you'll see that, since it is not that easy to divide, you may try to use the alternatives and what you already have to solve this problem.

The answer is an integer, so "one" number squared will give you 289. You already have 18 (from sq. root 324), and the last digit of 289 is 9. So the root must be 13 or 17 (because the digits will give the 9 digit when multiplied). 18 + 13 is 31, so NO. 18 + 17 will give you 35, so answer D.
Retired Moderator Joined: 16 Jun 2012
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My 20 seconds approach. Hope it helps.

When see questions about square/square root, think about "last digit" approach. It helps you save a lot of time.

Last digit of 324 = 4. Sqrt of 4 is 2.
Last digit of 289 = 9. Sqrt of 9 is 3

Last digit of the sum MUST be 5 (2+3 = 5). Only D is correct.

You don't need to figure out what sqrt of 324 or sqrt of 289 are.

Hope it helps.
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Intern  Joined: 09 Nov 2014
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pqhai, "When see questions about square/square root, think about "last digit" approach. It helps you save a lot of time."

Why does this approach work?
Intern  Joined: 12 Apr 2014
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All the answers choices are INTEGERS, so both the Numbers should be perfect squares. Since unit's digit of 289 is 9, unit's digit of its square root should be 7 or 3. So, 13^2 = 169, 17^2 = 289.
An easy way to find square of number -

Numbers having 5 as unit's digit --> 35^2 == 3*(3+1),5*5 => 3*4,25 => 12,25
65^2 == 6*(6+1),5*5 => 6*7,25 => 42,25
115^2 == 11*12,25 => 132,25

Numbers having Non-5 as unit's Digits --> 37^2 == 35^2 + 2(35+37) = 1225 + 144 = 1369
76^2 == 75^2 + (75+76) = 5625 + 151 = 5776
33^2 == 30^2 + 3(30+33) = 1089
Retired Moderator Joined: 06 Jul 2014
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GMAT 1: 660 Q48 V33 GMAT 2: 740 Q50 V40 Show Tags

pqhai wrote:
My 20 seconds approach. Hope it helps.

When see questions about square/square root, think about "last digit" approach. It helps you save a lot of time.

Last digit of 324 = 4. Sqrt of 4 is 2.
Last digit of 289 = 9. Sqrt of 9 is 3

Last digit of the sum MUST be 5 (2+3 = 5). Only D is correct.

You don't need to figure out what sqrt of 324 or sqrt of 289 are.

Hope it helps.

I'm not sure that this is completely right approach.
For example we have numbers 81 and 25

Last digit of 81 = 1. Sqrt of 1 is 1
Last digit of 25 = 5. Sqrt of 5 is 5

Last digit of sum should be 1 + 5 = 6
But sum of roots is 9 + 5 = 14

Or we can take numbers 576 and 144

Last digit of 576 = 6. Sqrt of 6 is 6
Last digit of 144 = 4. Sqrt of 4 is 2

Last digit of sum should be 6 + 2 = 8
But sum of roots is 24 + 12 = 36
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The square root of 5 is not 5 buddy.
Intern  Joined: 01 Jan 2018
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How are we calculating square root of 5 as 5 and square root of 6 as 6? Re: D01-01   [#permalink] 28 Mar 2018, 18:25
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