Bunuel wrote:
\(\sqrt{98}+ \sqrt{72} =\)
A. \(\sqrt{170}\)
B. \(\sqrt{232}\)
C. \(\sqrt{286}\)
D. \(\sqrt{338}\)
E. \(\sqrt{420}\)
We can also solve this question with some
approximationHere 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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