Question
Write \( 3 \sqrt{10} \) using rational exponents
Ask by Munoz Burton. in the United States
Feb 24,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
\( 3 \times 10^{1/2} \)
Solution
Recall that the square root of a number can be written as that number raised to the power of ½. Thus,
√10 = 10^(1/2).
So, the expression 3√10 written with rational exponents is:
3 · 10^(1/2).
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Simplify this solution The Deep Dive
To express \( 3 \sqrt{10} \) using rational exponents, we first recognize that the square root can be rewritten as an exponent. Specifically, the square root of 10 can be expressed as \( 10^{1/2} \). Therefore, we have: \[ 3 \sqrt{10} = 3 \times 10^{1/2} \] In this case, \( 3 \) remains as a coefficient, and \( \sqrt{10} \) is represented as \( 10^{1/2} \). So, the final expression is: \[ 3 \sqrt{10} = 3 \times 10^{1/2} \]
