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Arithmetic- roots

This topic has 4 expert replies and 0 member replies

Arithmetic- roots

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√98+√72=

A. √170
B. √232
C. √286
D. √338
E. √420
oa is d
Can some experts help me with this? Thanks

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Roland2rule wrote:
√98+√72=

A. √170
B. √232
C. √286
D. √338
E. √420
oa is d
Can some experts help me with this? Thanks
√98 = √49 * √2 =. 7√2
√72 = √36 * √2 =. 6√2

√98+√72 = 7√2 + 6√2 = 13√2 = √(2 * 13^2) = √(2 * 169) =√338. The answer is D

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GMAT/MBA Expert

Post
Roland2rule wrote:
√98+√72=

A. √170
B. √232
C. √286
D. √338
E. √420
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"
√49 = 7
√64 = 8
√81 = 9
√100 = 10

Since √98 is BETWEEN √81 and √100, we know that √98 is BETWEEN 9 and 10
Also, since √98 is VERY CLOSE to √100, we can conclude that √98 is much closer to 10 than it is to 9
So, we might say that √98 ≈ 9.8 or 9.9

Likewise, since √72 is BETWEEN √64 and √81, we know that √72 is BETWEEN 8 and 9
Here, √72 is pretty much halfway between √64 and √81, we might say that √72 ≈ 8.5

NOTE: As we'll soon see, we don't need to be super accurate with our approximations.
We have: √98 + √72 ≈ 9.9 + 8.5 = ≈18.4

Now let's examine a few more "nice" roots"
17² = 289. So, √289 = 17
18² = 324. So, √324 = 18
19² = 361. So, √361 = 19
Since 18.4 is BETWEEN 18 and 19, we're looking for an answer choice that is BETWEEN √324 and √361
Since √338 is the ONLY answer choice BETWEEN √324 and √361, the correct answer must be D

Cheers,
Brent

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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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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....

Final Answer: D

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