Simplify Cube Roots Expression

The problem requires simplifying the expression involving cube roots of decimal numbers: $\sqrt[3]{0.216} + \sqrt[3]{0.001} - \sqrt[3]{0.008}$.

Calculate Individual Cube Roots

We need to find the value of each cube root separately:

• To find $\sqrt[3]{0.216}$: Recognize that $6^3 = 216$. Therefore, $0.6^3 = 0.6 \times 0.6 \times 0.6 = 0.216$. So, $\sqrt[3]{0.216} = 0.6$.
• To find $\sqrt[3]{0.001}$: Recognize that $1^3 = 1$. Therefore, $0.1^3 = 0.1 \times 0.1 \times 0.1 = 0.001$. So, $\sqrt[3]{0.001} = 0.1$.
• To find $\sqrt[3]{0.008}$: Recognize that $2^3 = 8$. Therefore, $0.2^3 = 0.2 \times 0.2 \times 0.2 = 0.008$. So, $\sqrt[3]{0.008} = 0.2$.

Combine Results

Now, substitute these values back into the original expression:

$ \sqrt[3]{0.216} + \sqrt[3]{0.001} - \sqrt[3]{0.008} = 0.6 + 0.1 - 0.2 $

Perform the arithmetic operations:

• Add the first two terms: $0.6 + 0.1 = 0.7$.
• Subtract the third term from the result: $0.7 - 0.2 = 0.5$.

The simplified value of the expression is $0.5$.