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100 points for $49 worth of Veritas practice GMATs FREE VERITAS PRACTICE GMAT EXAMS Earn 10 Points Per Post Earn 10 Points Per Thanks Earn 10 Points Per Upvote ## Arithmetic- roots tagged by: Brent@GMATPrepNow ##### This topic has 4 expert replies and 0 member replies ## Arithmetic- roots âˆš98+âˆš72= A. âˆš170 B. âˆš232 C. âˆš286 D. âˆš338 E. âˆš420 oa is d Can some experts help me with this? Thanks ### GMAT/MBA Expert Legendary Member Joined 14 Jan 2015 Posted: 2666 messages Followed by: 125 members Upvotes: 1153 GMAT Score: 770 Roland2rule wrote: âˆš98+âˆš72= A. âˆš170 B. âˆš232 C. âˆš286 D. âˆš338 E. âˆš420 oa is d Can some experts help me with this? Thanks âˆš98 = âˆš49 * âˆš2 =. 7âˆš2 âˆš72 = âˆš36 * âˆš2 =. 6âˆš2 âˆš98+âˆš72 = 7âˆš2 + 6âˆš2 = 13âˆš2 = âˆš(2 * 13^2) = âˆš(2 * 169) =âˆš338. The answer is D _________________ Veritas Prep | GMAT Instructor Veritas Prep Reviews Save$100 off any live Veritas Prep GMAT Course

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### GMAT/MBA Expert

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Roland2rule wrote:
âˆš98+âˆš72=

A. âˆš170
B. âˆš232
C. âˆš286
D. âˆš338
E. âˆš420
oa is d
Can some experts help me with this? Thanks
We can also solve this question with some approximation
Here are a few "nice" roots"
âˆš49 = 7
âˆš64 = 8
âˆš81 = 9
âˆš100 = 10

Since âˆš98 is BETWEEN âˆš81 and âˆš100, we know that âˆš98 is BETWEEN 9 and 10
Also, since âˆš98 is VERY CLOSE to âˆš100, we can conclude that âˆš98 is much closer to 10 than it is to 9
So, we might say that âˆš98 â‰ˆ 9.8 or 9.9

Likewise, since âˆš72 is BETWEEN âˆš64 and âˆš81, we know that âˆš72 is BETWEEN 8 and 9
Here, âˆš72 is pretty much halfway between âˆš64 and âˆš81, we might say that âˆš72 â‰ˆ 8.5

NOTE: As we'll soon see, we don't need to be super accurate with our approximations.
We have: âˆš98 + âˆš72 â‰ˆ 9.9 + 8.5 = â‰ˆ18.4

Now let's examine a few more "nice" roots"
17Â² = 289. So, âˆš289 = 17
18Â² = 324. So, âˆš324 = 18
19Â² = 361. So, âˆš361 = 19
Since 18.4 is BETWEEN 18 and 19, we're looking for an answer choice that is BETWEEN âˆš324 and âˆš361
Since âˆš338 is the ONLY answer choice BETWEEN âˆš324 and âˆš361, the correct answer must be D

Cheers,
Brent

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### GMAT/MBA Expert

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Hi Roland2rule,
Let's take a look at your question.

$$\sqrt{98}+\sqrt{72}=?$$
Simplify the square roots,

$$=\sqrt{2\times7\times7}+\sqrt{2\times6\times6}$$
$$=7\sqrt{2}+6\sqrt{2}$$
$$=\sqrt{2}\left(7+6\right)$$
$$=13\sqrt{2}$$
$$=\sqrt{2\times13\times13}$$
$$=\sqrt{338}$$

Therefore, Option D is correct.
Hope this helps.

I am available, if you'd like any follow up.

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### GMAT/MBA Expert

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Hi Roland2rule,

While this question might look a bit 'scary', the answer choices are 'spread out' enough that you can use them 'against' the prompt, do a bit of estimation and get the correct answer without too much trouble.

To start, 98 is fairly close to 100, so we can estimate the value of the first radical to be 10.
In addition, 72 is clearly more than 64, so we know that the value of the second radical is a bit more than 8.
Thus, we're looking for an answer that's fairly close to 18.

18^2= 324 and there's only one answer that's close to that....

GMAT assassins aren't born, they're made,
Rich

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