Fill in the blanks in the following proof that the square

Chapter 4, Problem 12E

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QUESTION:

Fill in the blanks in the following proof that the square of any rational number is rational:

Proof: Suppose that r is By definition of rational, r = a/b for some with \(b \neq 0\). By substitution,

\(r^{2}\) = = \(a^{2} / b^{2}\).

Since a and b are both integers, so are the products \(a^{2}\) and Also \(b^{2} \neq 0\) by the  Hence \(r^{2}\) is a ratio of two integers with a non zero denominator, and so definition of rational.

Text Transcription:

b neq 0

r^2

a^2 / b^2

a^2

b^2 neq 0

Questions & Answers

QUESTION:

Fill in the blanks in the following proof that the square of any rational number is rational:

Proof: Suppose that r is By definition of rational, r = a/b for some with \(b \neq 0\). By substitution,

\(r^{2}\) = = \(a^{2} / b^{2}\).

Since a and b are both integers, so are the products \(a^{2}\) and Also \(b^{2} \neq 0\) by the  Hence \(r^{2}\) is a ratio of two integers with a non zero denominator, and so definition of rational.

Text Transcription:

b neq 0

r^2

a^2 / b^2

a^2

b^2 neq 0

ANSWER:

Solution : Step 1 : In this problem we have to fill the blanks

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