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tester [92]
11 months ago
10

N is a rational number.m is an irrational number.n2 cannot be an irrational number? why or why not

Mathematics
1 answer:
Korolek [52]11 months ago
8 0

If n is rational, it means that

n\in\mathbb{Q}\Rightarrow n=\frac{p}{q},\quad p\in\mathbb{Z},\quad q\in\mathbb{Z}^*

Therefore when we do n² we can write it as

n^2=\frac{p^2}{q^2},\quad p\in\mathbb{Z},\quad q\in\mathbb{Z}^*

Remember that the product of two integer numbers is also an integer, therefore we can guarantee that

p^2\in\mathbb{Z}\text{ and }q^2\in\mathbb{Z}^*

Then we can confirm that n² is the quotient of two integers and the denominator is not zero, therefore, n² is always rational, it cannot be an irrational number

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