Question

jillian said \\(\sqrt{25}\\) is irrational because it is a square root. why is she incorrect?

jillian is incorrect because the square root of \\(\sqrt{25} = 5.5\\).
jillian is incorrect because a square root is always rational.
jillian is incorrect because square roots of perfect squares are rational.
jillian is incorrect because the decimal expansion of \\(\sqrt{25}\\) is a repeating decimal.

Explanation:

Evaluate the square root of 25

$$ \sqrt{25} = 5 $$

Classify the resulting value

$$ 5 = \frac{5}{1} \in \mathbb{Q} $$

Identify the correct explanation

$$ 25 = 5^2 \implies \text{square roots of perfect squares are rational} $$

Answer:

• (A) Jillian is incorrect because the square root of \(\sqrt{25} = 5.5\).
• (B) Jillian is incorrect because a square root is always rational.
• (C) Jillian is incorrect because square roots of perfect squares are rational. (Correct answer)
• (D) Jillian is incorrect because the decimal expansion of \(\sqrt{25}\) is a repeating decimal.