Let's evaluate the expression [tex]\(\sqrt{\frac{9}{8}}\)[/tex] given that [tex]\(\sqrt{72} = 8.485\)[/tex].
### Step-by-step solution:
1. Understand the given value:
- We are provided with [tex]\(\sqrt{72}\)[/tex], which is approximately 8.485.
2. Simplify [tex]\(\sqrt{\frac{9}{8}}\)[/tex] using the given [tex]\(\sqrt{72}\)[/tex]:
- To proceed, we need to manipulate the expression [tex]\(\sqrt{\frac{9}{8}}\)[/tex].
3. Consider simplification and transformations:
- Recall that [tex]\(\sqrt{\frac{a}{b}} = \frac{\sqrt{a}}{\sqrt{b}}\)[/tex].
- Therefore, [tex]\(\sqrt{\frac{9}{8}}\)[/tex] can be rewritten as:
[tex]\[
\sqrt{\frac{9}{8}} = \frac{\sqrt{9}}{\sqrt{8}}
\][/tex]
4. Calculate individual square roots:
- The value [tex]\(\sqrt{9} = 3\)[/tex].
- The value [tex]\(\sqrt{8} = \sqrt{\frac{72}{9}}\)[/tex], because [tex]\(8 = \frac{72}{9}\)[/tex].
5. Use the given value to find [tex]\(\sqrt{8}\)[/tex]:
- Given [tex]\(\sqrt{72} \approx 8.485\)[/tex], we know [tex]\(8.485 = \sqrt{72} \approx \sqrt{9 \times 8}\)[/tex].
- Hence, [tex]\(\sqrt{8}\)[/tex] can be found by:
[tex]\[
\sqrt{8} \approx \frac{8.485}{3} \approx 2.828
\][/tex]
6. Final Calculation:
- Now, substitute [tex]\(\sqrt{9} = 3\)[/tex] and [tex]\(\sqrt{8} \approx 2.828\)[/tex] back into the simplified form:
[tex]\[
\sqrt{\frac{9}{8}} = \frac{3}{2.828} \approx 1.060
\][/tex]
Therefore, the correct value of [tex]\(\sqrt{\frac{9}{8}}\)[/tex], given that [tex]\(\sqrt{72} = 8.485\)[/tex], is approximately 1.060. Hence, the correct option is:
(d) 1.060
