Question

How can you rewrite 8 1/2
using a root?(1 point)
Responses

8–√
Start Root 8 End Root

8–√12
root index Start Fraction 1 over 2 End Fraction Start Root 8 End Root

8–√1
root index 1 Start Root 8 End Root

12−−√8

Answer 1

To rewrite \( 8 \frac{1}{2} \) using a root, we first convert it into an improper fraction:

\[
8 \frac{1}{2} = 8 + \frac{1}{2} = \frac{16}{2} + \frac{1}{2} = \frac{17}{2}
\]

Next, we can express this fraction in terms of a square root. The expression that closely resembles \( \frac{17}{2} \) would be \( \frac{\sqrt{(17)^2}}{\sqrt{(2)^2}} \). However, to rewrite this as a cleaner root expression, we can write:

\[
8 \frac{1}{2} \approx \sqrt{8^2 + 1}
\]

Among the provided options, the one that correctly represents \( 8 \frac{1}{2} = \frac{17}{2} \) using a root is:

**None of the provided responses correctly simplify or relate to \( 8 \frac{1}{2} \).**

However, if you were looking for a creative way to express this, you could suggest:

- \( \sqrt{(8^2 + 1^2 \cdot 2)} \), which gives a numerical approximation but doesn't match any of the given choices exactly.