Question
According to exponent rules, what is the rational exponent in the equivalent expression to 3 square root five. Explain your response in fraction form
Answers
Answered by
GPT-4o mini
To express \( 3 \sqrt{5} \) using rational exponents, let's break it down step by step.
1. We start with the square root of a number. The square root of any number \( x \) can be expressed as \( x^{1/2} \).
2. Therefore, the square root of 5 can be written as:
\[
\sqrt{5} = 5^{1/2}
\]
3. Now, substituting this back into the expression \( 3 \sqrt{5} \), we have:
\[
3 \sqrt{5} = 3 \cdot 5^{1/2}
\]
4. In this case, we can also represent this as:
\[
3 \sqrt{5} = 3 \cdot 5^{1/2} = 3 \cdot 5^{0.5}
\]
Therefore, rational exponent associated with this expression, specifically for \( \sqrt{5} \), is \( \frac{1}{2} \).
In summary, the rational exponent for the square root of 5 in the expression \( 3 \sqrt{5} \) is \( \frac{1}{2} \).
1. We start with the square root of a number. The square root of any number \( x \) can be expressed as \( x^{1/2} \).
2. Therefore, the square root of 5 can be written as:
\[
\sqrt{5} = 5^{1/2}
\]
3. Now, substituting this back into the expression \( 3 \sqrt{5} \), we have:
\[
3 \sqrt{5} = 3 \cdot 5^{1/2}
\]
4. In this case, we can also represent this as:
\[
3 \sqrt{5} = 3 \cdot 5^{1/2} = 3 \cdot 5^{0.5}
\]
Therefore, rational exponent associated with this expression, specifically for \( \sqrt{5} \), is \( \frac{1}{2} \).
In summary, the rational exponent for the square root of 5 in the expression \( 3 \sqrt{5} \) is \( \frac{1}{2} \).