Solution Found!
Fill in the blanks in the following proof that the square
Chapter 4, Problem 12E(choose chapter or problem)
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