AbdurRakib wrote:

Which of the following is greatest?

A. \(10\sqrt{3}\)

B. \(9\sqrt{4}\)

C. \(8\sqrt{5}\)

D. \(7\sqrt{6}\)

E. \(6\sqrt{7}\)

Let’s estimate √3, √5, √6, and √7.

√3 ≈ 1.7

√5 ≈ 2.2

√6 ≈ 2.4

√7 ≈ 2.7

Thus:

A) 10 x 1.7 = 17

B) 9 x 2 = 18

C) 8 x 2.2 = 17.6

D) 7 x 2.4 = 16.8

E) 6 x 2.7 = 16.2

Alternate Solution:

Another way to get rid of the roots to compare each answer is to square each answer choice:

A) (10√3)^2 = 100 x 3 = 300

B) (9√4)^2 = 81 x 4 = 324

C) (8√5)^2 = 64 x 5 = 320

D) (7√6)^2 = 49 x 6 = 294

E) (6√7)^2 = 36 x 7 = 252

Answer: B

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