To determine which of the given values is the greatest, let's evaluate each one step by step:
1. Option (a): [tex]\( (0.01)^{1/2} \)[/tex]
- This represents the square root of 0.01.
- The square root of 0.01 is 0.1.
2. Option (b): [tex]\( (0.2)^2 \)[/tex]
- This represents 0.2 raised to the power of 2.
- Calculating [tex]\( 0.2^2 \)[/tex] gives 0.04.
3. Option (c): [tex]\( \frac{1}{100} \)[/tex]
- This represents the fraction 1 divided by 100.
- Performing this division, we get 0.01.
4. Option (d): [tex]\( (0.008)^{1/3} \)[/tex]
- This represents the cube root of 0.008.
- The cube root of 0.008 is 0.2.
After calculating each value, we have:
- [tex]\( (0.01)^{1/2} = 0.1 \)[/tex]
- [tex]\( (0.2)^2 = 0.04 \)[/tex]
- [tex]\( \frac{1}{100} = 0.01 \)[/tex]
- [tex]\( (0.008)^{1/3} = 0.2 \)[/tex]
Now, let's compare these values:
- 0.1
- 0.04
- 0.01
- 0.2
Among these numbers, 0.2 is the greatest.
Therefore, the option with the greatest value is:
Option (d): [tex]\( (0.008)^{1/3} \)[/tex]
So, the correct answer is:
D. d
