Question

sam said the square root of a rational number must be a rational number. jenna disagreed. she said that it is possible that the square root of a rational number can be irrational. who is correct and why?

jenna is correct because all square roots are irrational numbers.
sam is correct because all square roots of rational numbers are rational. an example is \\(\sqrt{121} = 11\\).
jenna is correct because not all square roots are rational. an example is \\(\sqrt{2} = 1.414213...\\).
sam is correct because the properties of square roots state that the square root of a rational number is a rational number.

Explanation:

Analyze the claims of Sam and Jenna

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Evaluate with a counterexample

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Match with the correct option

$$ \text{Jenna is correct because not all square roots are rational. An example is } \sqrt{2} = 1.414213\dots $$

Answer:

• Jenna is correct because all square roots are irrational numbers.
• Sam is correct because all square roots of rational numbers are rational. An example is \(\sqrt{121} = 11\).
• Jenna is correct because not all square roots are rational. An example is \(\sqrt{2} = 1.414213\dots\) (Correct answer)
• Sam is correct because the properties of square roots state that the square root of a rational number is a rational number.