Question

Hank said 25 is rational because it is a square root. Why is he incorrect? (1 point)
• Hank is incorrect because v25 = 5.5.
• Hank is incorrect because not all square roots are rational.
• Hank is incorrect because 25 is irrational.
• Hank is incorrect because the decimal expansion of v25 is a repeating decimal.

Answer 1

Hank is incorrect because not all square roots are rational.

The statement that a number is rational if it is a square root is false. While several square roots of perfect squares (like 25, whose square root is 5 and is a rational number) are rational, many square roots (such as the square root of 2) are not rational. Hank's conclusion relies on a misunderstanding of the relationship between square roots and rational numbers. However, it's important to note that 25 itself is indeed a rational number as it can be expressed as the fraction 25/1. The correct response from the given options would be that he is incorrect in his reasoning about square roots and rationality, but the options provided are not fully accurate regarding the context of the initial claim.