Question
How can you rewrite 9
1/3
using a root?(1 point)
1/3
using a root?(1 point)
Answers
GPT-4o mini
To rewrite \( 9 \frac{1}{3} \) using a root, first convert the mixed number into an improper fraction.
1. Convert \( 9 \frac{1}{3} \) to an improper fraction:
\[
9 \frac{1}{3} = \frac{27}{3} + \frac{1}{3} = \frac{28}{3}
\]
2. Next, express \( \frac{28}{3} \) using roots. You can express it as a root by noticing that \( 28 \) can be represented in terms of a square root:
\[
\frac{28}{3} = \frac{4 \times 7}{3} = \frac{4}{3} \times 7
\]
However, if you're looking for a more direct expression involving roots, you can write \( 28 \) in terms of its square root:
\[
28 = 4 \times 7 = \sqrt{(4 \times 7)^2} = \sqrt{28^2}
\]
Thus, one way to express it involving a root is:
\[
9 \frac{1}{3} = \frac{28}{3} \approx \sqrt{28}^2 \div 3
\]
For simplicity and given that \( \sqrt{(\frac{28}{3})}^2 \) directly may not yield the cleanest form, the answer simplifies to saying \( 9 \frac{1}{3} \) can be expressed as \( \frac{28}{3} \) or involving computations, as mentioned above. Adjust accordingly to context if needed!
In summary, the representation can differ, but a clean expression involving roots specifically may require numerical values instead.
1. Convert \( 9 \frac{1}{3} \) to an improper fraction:
\[
9 \frac{1}{3} = \frac{27}{3} + \frac{1}{3} = \frac{28}{3}
\]
2. Next, express \( \frac{28}{3} \) using roots. You can express it as a root by noticing that \( 28 \) can be represented in terms of a square root:
\[
\frac{28}{3} = \frac{4 \times 7}{3} = \frac{4}{3} \times 7
\]
However, if you're looking for a more direct expression involving roots, you can write \( 28 \) in terms of its square root:
\[
28 = 4 \times 7 = \sqrt{(4 \times 7)^2} = \sqrt{28^2}
\]
Thus, one way to express it involving a root is:
\[
9 \frac{1}{3} = \frac{28}{3} \approx \sqrt{28}^2 \div 3
\]
For simplicity and given that \( \sqrt{(\frac{28}{3})}^2 \) directly may not yield the cleanest form, the answer simplifies to saying \( 9 \frac{1}{3} \) can be expressed as \( \frac{28}{3} \) or involving computations, as mentioned above. Adjust accordingly to context if needed!
In summary, the representation can differ, but a clean expression involving roots specifically may require numerical values instead.