To rewrite \( 9 \frac{1}{3} \) using a square root, we first convert the mixed number into an improper fraction.
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Convert \( 9 \frac{1}{3} \) to an improper fraction: \[ 9 \frac{1}{3} = \frac{27}{3} + \frac{1}{3} = \frac{28}{3} \]
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It's mentioned that the number isn't \( \frac{28}{3} \), so we can represent it in a different way involving square roots.
One way to express \( 9 \frac{1}{3} \) using a square root is to think of it as: \[ 9 \frac{1}{3} = 9 + \frac{1}{3} = 9 + \sqrt{\frac{1}{9}} \]
Another option is to find a number that relates to \( 9 \frac{1}{3} \) through a square root. The value of \( 9 \frac{1}{3} \) is approximately \( 9.33 \). We can find a square root that yields to close either to this value or expresses its equivalent.
For a cleaner mathematical representation without actually evaluating to \( \frac{28}{3} \), you can say: \[ 9 \frac{1}{3} = \frac{27 + \sqrt{1}}{3} \]
If you have any specific restrictions or types of roots you need (like using cube roots instead), please specify!
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