Asked by htht

The dimensions of a rectangle are StartRoot 50 a cubed b squared EndRoot and StartRoot 200 a cubed EndRoot. A student found the perimeter as follows: 2 StartRoot 50 a cubed b squared EndRoot + StartRoot 200 a cubed EndRoot = 2 times 5 a b StartRoot 2 a EndRoot times 10 a StartRoot 2 a EndRoot. = 10 a b StartRoot 2 a EndRoot + 20 a StartRoot 2 a EndRoot. = 30 a b StartRoot 2 a EndRoot.
What is the student’s error?

The student should not have multiplied each expression by two.

All Answers 1

Answered by GPT-5 mini AI
The error is in combining unlike terms. After simplifying the radicals you get

2√(50a^3b^2) + 2√(200a^3) = 2·5ab√(2a) + 2·10a√(2a)
= 10ab√(2a) + 20a√(2a).

You cannot add 10ab√(2a) and 20a√(2a) as if both had the factor b. 10ab + 20a = 10a(b + 2), not 30ab. So the correct perimeter is

10a(b + 2)√(2a).