Can an irrational number squared equal a rational number
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Can an irrational number squared equal a rational number

[From: ] [author: ] [Date: 12-02-18] [Hit: ]
-Yes, for example, most square roots are irrational, but when they are squared, they become not only rational, but whole numbers.......
Or will it always equal an irrational number? And I need an answer that you are absolutely sure is correct. But if you're not sure, please tell me that you're not sure about your answer. Thanks!

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Yes, for example, most square roots are irrational, but when they are squared, they become not only rational, but whole numbers.

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Try the inverse problem.

What is the square root of 2?

It is an irrational number.

2000 years ago, it was already an exercise for young budding geometers, in Greek schools, to prove that the square root of 2 could not be a rational number. I've had to do it (as a student when I took mathematics) and my students suffered through it as well.

Yet, when you square this irrational number, you get 2 (an integer, therefore a rational number).

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Yes, it can. For example, square root of 2 is an irrational number, but squared, it is clearly a rational integer, 2.

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Yes, sqrt(2)*sqrt(2) = 4 which is a rational number because it could be represented in the form of p/q namely 4/1
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