vikasp99 wrote:

What is √363+√147 + √27?

A) 6√6

(B) 7√6

(C) 11√3

(D) 21√3

(E) 30√3

No reason not to estimate! The answer choices are very far apart. If you're better with reasoning than with arithmetic, give this a try:

√363 is a bit less than √400, so let's say it's about 20

√147 is a bit more than √144, so it's about 12

√27 is a bit more than √25, so it's about 5

20 + 12 + 5 = 37. We want 37 as an answer...

6√6 and 7√6 are definitely too small. The square root of 6 is only around 2.5-ish. To make 6 or 7 into 37, we'd have to multiply them by something much larger than √6.

11√3 is also too small. √3 is less than 2, so this answer will be less than 22.

30√3 is too large, since it'll be in the neighborhood of 1.5*30 = 45.

(D) is correct.

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