Question
What rational exponent could be used to express
3
square root 23
?
3
square root 23
?
Answers
GPT-4o mini
To express the square root of a number with a rational exponent, you can use the exponent \( \frac{1}{2} \).
For the expression \( 3 \sqrt{23} \), you can rewrite the square root of \( 23 \) using the rational exponent:
\[
\sqrt{23} = 23^{\frac{1}{2}}
\]
Thus, the expression \( 3 \sqrt{23} \) can be expressed as:
\[
3 \sqrt{23} = 3 \cdot 23^{\frac{1}{2}}
\]
So, the rational exponent you would use to express \( \sqrt{23} \) is \( \frac{1}{2} \).
For the expression \( 3 \sqrt{23} \), you can rewrite the square root of \( 23 \) using the rational exponent:
\[
\sqrt{23} = 23^{\frac{1}{2}}
\]
Thus, the expression \( 3 \sqrt{23} \) can be expressed as:
\[
3 \sqrt{23} = 3 \cdot 23^{\frac{1}{2}}
\]
So, the rational exponent you would use to express \( \sqrt{23} \) is \( \frac{1}{2} \).