Question

If the length of a rectangle is given the expression 2 square root of 153 and the width is given by 4 square root of 68, which radical expression represents the perimeter of the rectangle

Answer 1

Answer:
C) 28√17
Explanation:
The perimeter is twice the sum of the two given side lengths, so is ...
P = 2(L +W) = 2(2√153 +4√68)
= 2(6√17 +8√17) = 2(14√17)
P = 28√17 . . . . . matches choice C
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This is about simplifying radicals. The applicable rules are ...
√(ab) = (√a)(√b)
√(a²) = |a|
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153 = 9×17, so √153 = (√9)(√17) = 3√17
68 = 4×17, so √68 = (√4)(√17) = 2√17
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Comment on the problem presentation
It would help if there were actually radicals in the radical expressions. We had to guess based on the spacing and the answer choices.
In any event, this problem can be worked with a calculator. Find the perimeter (≈115.45) and see which answer matches that. (That's what I did in order to verify my understanding of what the radical expressions were.)