Sure, let's go through each part of the question step-by-step.
### e) [tex]\(\left(\frac{2}{5} \times \frac{3}{4} \times \frac{5}{6}\right)^2\)[/tex]
Step 1: Multiply the fractions together.
[tex]\[
\frac{2}{5} \times \frac{3}{4} \times \frac{5}{6} = \frac{2 \cdot 3 \cdot 5}{5 \cdot 4 \cdot 6}
\][/tex]
Step 2: Simplify the numerator and the denominator.
[tex]\[
\frac{2 \cdot 3 \cdot 5}{5 \cdot 4 \cdot 6} = \frac{30}{120} = \frac{1}{4}
\][/tex]
Step 3: Square the result.
[tex]\[
\left(\frac{1}{4}\right)^2 = \frac{1}{16} = 0.0625
\][/tex]
So the result for part (e) is:
[tex]\[
0.0625
\][/tex]
### 1) [tex]\(\frac{6}{7} - \frac{4}{5}\)[/tex]
Step 1: Find a common denominator for the fractions, which is 35.
[tex]\[
\frac{6}{7} = \frac{6 \times 5}{7 \times 5} = \frac{30}{35}
\][/tex]
[tex]\[
\frac{4}{5} = \frac{4 \times 7}{5 \times 7} = \frac{28}{35}
\][/tex]
Step 2: Subtract the fractions.
[tex]\[
\frac{30}{35} - \frac{28}{35} = \frac{30 - 28}{35} = \frac{2}{35} \approx 0.05714285714285705
\][/tex]
So the result for part (1) is:
[tex]\[
0.05714285714285705
\][/tex]
### 9) [tex]\(-0.24\)[/tex]
There is no operation to perform here, so the result is simply:
[tex]\[
-0.24
\][/tex]
### h) [tex]\(\sqrt{2}\)[/tex]
The square root of 2 is a well-known irrational number. Its approximate value is:
[tex]\[
1.4142135623730951
\][/tex]
So the result for part (h) is:
[tex]\[
1.4142135623730951
\][/tex]
Putting it all together, the detailed solutions for the given parts are:
e) [tex]\(0.0625\)[/tex]
1) [tex]\(0.05714285714285705\)[/tex]
9) [tex]\(-0.24\)[/tex]
h) [tex]\(1.4142135623730951\)[/tex]
