26. Se define en [tex]\( Z \)[/tex]:
[tex]\[
\left[\frac{\sqrt{b}}{a}\right]=a^2 \times \sqrt[4]{b}
\][/tex]

Calcule:

[tex]\[
\begin{tabular}{|c|}
\hline
4 \\
\hline
9 \\
\hline
\sqrt{2} \\
\hline
\end{tabular}
\][/tex]

a. 70
b. 62
c. 72
d. 60
e. 65



Answer :

To solve the problem defined by the expression [tex]\(\left[\frac{\sqrt{b}}{a}\right]=a^2 \times \sqrt[4]{b}\)[/tex], follow these steps:

1. Identify the variables and numerical values:
- [tex]\(a = 4\)[/tex]
- [tex]\(b = 9\)[/tex]

2. Compute [tex]\(\sqrt{b}\)[/tex]:
- [tex]\(\sqrt{b} = \sqrt{9} = 3\)[/tex]

3. Compute the fourth root of [tex]\(b\)[/tex]:
- [tex]\(\sqrt[4]{b} = \sqrt[4]{9} = (9)^{1/4}\)[/tex]

4. Calculate [tex]\(\left[\frac{\sqrt{b}}{a}\right]\)[/tex] inside the brackets:
- Place the previously computed value of [tex]\(\sqrt{b}\)[/tex]:
[tex]\[ \left[\frac{3}{4}\right] \][/tex]
- Evaluate the expression inside the brackets but note that due to its construction, the actual calculation focuses on:
[tex]\[ a^2 \times \sqrt[4]{b} \][/tex]

5. Compute [tex]\(a^2\)[/tex]:
- [tex]\(a^2 = 4^2 = 16\)[/tex]

6. Combine the results:
- Multiply [tex]\(a^2\)[/tex] by [tex]\(\sqrt[4]{b}\)[/tex]:
- [tex]\(\sqrt[4]{9} = \)[/tex] the fourth root of 9 can be computed. For simplicity, assume this value impacts the overall multiplication correctly.

7. Final Calculation:
Given the components:
[tex]\[ 16 \times (9)^{1/4} \][/tex]
This results in approximately:
[tex]\[ 16 \times 1.732... \approx 27.7128 \][/tex]

8. Compare the calculated result with the provided choices:
- The calculated value is approximately [tex]\(27.7128\)[/tex]

So, comparing this value to the provided multiple-choice options, none of the choices [tex]\(70, 72, 60, 62, 65\)[/tex] match the computed value of approximately [tex]\(27.7128\)[/tex].

Thus, the final outcome is:
- [tex]\[ 27.7128 \][/tex]
- And there are no appropriate choices that match this value. Hence, the result includes an empty set for feasible choices.