Question
Luke thinks that √2¹⁰ is irrational. What do you think? Give reasons.
Answers
GPT-4o mini
To determine whether \( \sqrt{2^{10}} \) is rational or irrational, we can simplify the expression.
First, we simplify \( \sqrt{2^{10}} \):
\[
\sqrt{2^{10}} = 2^{10/2} = 2^5 = 32
\]
Since \( 32 \) is a whole number, it is a rational number (any integer is rational, as it can be expressed as a fraction of itself and 1, i.e., \( \frac{32}{1} \)).
Therefore, Luke's assertion that \( \sqrt{2^{10}} \) is irrational is incorrect. In conclusion, \( \sqrt{2^{10}} \) is rational.
First, we simplify \( \sqrt{2^{10}} \):
\[
\sqrt{2^{10}} = 2^{10/2} = 2^5 = 32
\]
Since \( 32 \) is a whole number, it is a rational number (any integer is rational, as it can be expressed as a fraction of itself and 1, i.e., \( \frac{32}{1} \)).
Therefore, Luke's assertion that \( \sqrt{2^{10}} \) is irrational is incorrect. In conclusion, \( \sqrt{2^{10}} \) is rational.