Let's break down the problem into clear steps to find the value of [tex]\(\sqrt[3]{0.0256^2}\)[/tex], and then we'll express this result to 3 significant figures.
### Step 1: Squaring the given value
The first step is to square the given value, which is 0.0256.
[tex]\[
(0.0256)^2 = 0.0256 \times 0.0256 = 0.00065536
\][/tex]
### Step 2: Finding the cube root
The next step is to find the cube root of the result obtained in Step 1.
[tex]\[
\sqrt[3]{0.00065536}
\][/tex]
To do this, we calculate:
[tex]\[
0.00065536^{\frac{1}{3}} \approx 0.08686136373103702
\][/tex]
### Step 3: Rounding to 3 significant figures
Now, we need to round this result to 3 significant figures. Here is the number before rounding:
[tex]\[
0.08686136373103702
\][/tex]
To round this number to 3 significant figures, we look at the first three digits:
[tex]\[
0.0868
\][/tex]
Since the digit after 8 is 6, we round up:
[tex]\[
\approx 0.087
\][/tex]
### Final Result:
Thus, [tex]\(\sqrt[3]{0.0256^2}\)[/tex] is approximately 0.087 when expressed to 3 significant figures.
