Back to Use square root and cube root symbols to represent solutions to equations — Problem 3 · Task Set 11

8.EE.A.2 Tutor Intake -- Square Roots and Cube Roots

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Concepts

A student computes $\sqrt{2} \approx 1.414$ on a calculator and
argues that $\sqrt{2}$ must be rational, since 1.414 is a
terminating decimal. What is wrong with this reasoning?

1.414 is only an approximation, not the exact value; the true decimal expansion of $\sqrt{2}$ goes on forever without repeating, which is what makes it irrational.

Nothing is wrong — since the calculator shows a terminating decimal, $\sqrt{2}$ is in fact rational.

The reasoning is wrong because $\sqrt{2}$ is actually a perfect square.

The reasoning is wrong because calculators cannot compute square roots accurately.