Question

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

Answer 1

Hank is incorrect because not all square roots are rational. Specifically, the square root of a number is rational only if that number is a perfect square. In this case, since $\sqrt{25}=5$, which is a rational number, Hank's reasoning overlooks that the claim was more about the general nature of square roots rather than specifically about $\sqrt{25}$. His statement implies that all square roots are rational, which is not true (for example, $\sqrt{2}$ is irrational). Therefore, the correct response is:

Hank is incorrect because not all square roots are rational.