17-04-2024
Mathematics

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is (sqrt(2))/(sqrt(2)) rational or irrational

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luclaporte2 luclaporte2

17-04-2024

Answer:

Rational

Step-by-step explanation:

When you divide a nonzero expression by itself, you always get 1.
1 by definition is a rational number because it can be expressed as a fraction.
e.g. 1/1, 5/5, x^2 / x^2 (except this expression is undefined when x is 0).
Given your example of (sqrt(2) / sqrt(2)), when you multiply the top by the bottom to rationalize the denominator, you get:

sqrt(2) * sqrt(2) / sqrt(2) * sqrt(2)
2 / 2
1

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