Question

whitch statment is true?

the root of 0.11 < (7/8)^3
the root of 0.11 > (7/8)^3
the root of 0.11 = (7/8)^3

Answer 1

To determine which statement is true, we first need to compute the values of \(\sqrt{0.11}\) and \((\frac{7}{8})^3\).

1. Calculate \(\sqrt{0.11}\):
\[
\sqrt{0.11} \approx 0.3317
\]

2. Calculate \((\frac{7}{8})^3\):
\[
\frac{7}{8} = 0.875
\]
\[
\left(\frac{7}{8}\right)^3 = 0.875^3 \approx 0.421875
\]

3. Compare the two values:
\[
\sqrt{0.11} \approx 0.3317 \quad \text{and} \quad \left(\frac{7}{8}\right)^3 \approx 0.421875
\]

Now we see that:
\[
0.3317 < 0.421875
\]

Thus, \(\sqrt{0.11} < \left(\frac{7}{8}\right)^3\).

The true statement is:
\[
\sqrt{0.11} < \left(\frac{7}{8}\right)^3
\]