Question

The approximate value of \( (0.007)^{1/3} \) is:

Hint:

For approximations of cube roots, use logarithmic estimates or nearby perfect cubes for an accurate estimate.

Answer 1

Step 1: Express the number in a simpler form

We are asked to find the approximate value of \( (0.007)^{1/3} \), which is the cube root of 0.007. We can rewrite this as: \[ (0.007)^{1/3} = (7 \times 10^{-3})^{1/3} \] This can be broken into: \[ (7 \times 10^{-3})^{1/3} = 7^{1/3} \times (10^{-3})^{1/3} \] Since \( (10^{-3})^{1/3} = 10^{-1} = 0.1 \), we now need to approximate \( 7^{1/3} \).

Step 2: Approximate the cube root of 7

The cube root of 7 is approximately \( 1.913 \). Therefore: \[ 7^{1/3} \approx 1.913 \]

Step 3: Multiply the results

Now, we multiply the approximate values: \[ (0.007)^{1/3} \approx 1.913 \times 0.1 = 0.1913 \]

Final Answer:

The approximate value of \( (0.007)^{1/3} \) is \( \boxed{0.191} \).