Question

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

Answer 1

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:

1. sqrt(2) * sqrt(2) / sqrt(2) * sqrt(2)
2. 2 / 2
3. 1

Hope this helps!