Answered: Why is the sum of the square roots of…

College Algebra (MindTap Course List)

12th Edition

ISBN:9781305652231

Author:R. David Gustafson, Jeff Hughes

Publisher:R. David Gustafson, Jeff Hughes

Chapter4: Polynomial And Rational Functions

Section4.1: Quadratic Functions

Problem 101E

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Why is the sum of the square roots of positive numbers always greater than the square root of their sum, but the sum of two squared numbers always less than the square of the sum of those same two numbers?

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That is not what I asked. I did not ask you to show me proof that it is true. A proof is not an explanation. Using words only, can you please explain to me why it is true that the sum of the square roots of positive numbers is always greater than the square root of their sum, but the sum of two squared numbers is always less than the square of the sum of those same two numbers?

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