√(16∗20+8∗32)=

M7MBA wrote:\(\sqrt{16\cdot 20+8\cdot 32}=\)

(A) \(4\sqrt{20}\)
(B) \(24\)
(C) \(25\)
(D) \(4\sqrt{20}+8\sqrt{2}\)
(E) \(32\)

[spoiler]OA=B[/spoiler]

Source: Official Guide

We must first simplify the expression in the square root before actually taking the square root. In other words, we have to get the product of 16 and 20 and add it to the product of 8 and 32 before taking the square root.

√[(16)(20) + (8)(32)]

√(320 + 256)

√576 = 24

Note: If you have trouble determining the value of √576, you could have used the answer choices to your advantage. Ask yourself what number, when squared, equals 576. Since we should have the value of 25^2 memorized, we would know that 25^2 = 625. Since 576 is slightly less than 625, we can reasonably determine that 24^2 = 576.

Alternate Solution:

Let’s begin by factoring the common factor of 8 under the radical sign:

√[(16)(20) + (8)(32)] = √[8(2*20 + 32] = √[8(40 + 32)]

Next, we factor another 8 from each term in the summation:

√[8(40 + 32)] = √[8*8(5 + 4)] = √[8*8*9] = [√(8*8)] * [√9]

The square root of 8*8 is 8 and the square root of 9 is 3; therefore, the answer is 8 * 3 = 24.

Answer: B