Question
What is the simplest form of 12513?(1 point)
Responses
125−−−√
square root of 125 - no response given
5
5 - no response given
1253−−−−√1
1th root of 125 cubed - no response given
41.66
Responses
125−−−√
square root of 125 - no response given
5
5 - no response given
1253−−−−√1
1th root of 125 cubed - no response given
41.66
Answers
GPT-4o mini
To simplify \( \sqrt{125} \):
1. Factor 125:
\[
125 = 5^3
\]
2. Apply the square root:
\[
\sqrt{125} = \sqrt{5^3} = \sqrt{5^2 \cdot 5} = \sqrt{25 \cdot 5} = \sqrt{25} \cdot \sqrt{5} = 5\sqrt{5}
\]
So, the simplest form of \( \sqrt{125} \) is \( 5\sqrt{5} \).
Since none of the provided responses include \( 5\sqrt{5} \), if you're looking for the numerical value, calculating \( \sqrt{125} \) gives approximately 11.18, which is not in the options either.
The closest option available to simplify \( \sqrt{125} \) is \( 5 \), but it's not the complete simplification. Therefore, if answering directly from the choices provided, the best answer would be if just '5' is mentioned (although it's not correct without including \( \sqrt{5} \)).
1. Factor 125:
\[
125 = 5^3
\]
2. Apply the square root:
\[
\sqrt{125} = \sqrt{5^3} = \sqrt{5^2 \cdot 5} = \sqrt{25 \cdot 5} = \sqrt{25} \cdot \sqrt{5} = 5\sqrt{5}
\]
So, the simplest form of \( \sqrt{125} \) is \( 5\sqrt{5} \).
Since none of the provided responses include \( 5\sqrt{5} \), if you're looking for the numerical value, calculating \( \sqrt{125} \) gives approximately 11.18, which is not in the options either.
The closest option available to simplify \( \sqrt{125} \) is \( 5 \), but it's not the complete simplification. Therefore, if answering directly from the choices provided, the best answer would be if just '5' is mentioned (although it's not correct without including \( \sqrt{5} \)).