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 $0.5$.
Important Questions from Simplification
Simplify the following expression.
\(\left(\frac{7}{16} \div \frac{1}{2}\:of\: \frac{1}{5}\right)\times \frac{4}{5}-\frac{1}{3}\times\frac{5}{8}\div \frac{1}{2}+\frac{3}{4}\)
The value of \(\left( {2\frac{6}{7}of4\frac{1}{5} \div \frac{2}{3}} \right) \times 5\frac{1}{9} \div \left( {\frac{3}{4} \times 2\frac{2}{3}of\frac{1}{2} \div \frac{1}{4}} \right)\) is:
The value of \(\left[ {\frac{4}{7}\rm \;of\;2\frac{4}{5} \times 1\frac{2}{3} - \left( {3\frac{1}{2} - 2\frac{1}{6}} \right)} \right] \div \left( {3\frac{1}{5} \div 4\frac{1}{2}\;\rm of\;\;5\frac{1}{3}} \right)\) is:
The value of \(\frac{{0.0203 \times 2.92}}{{0.7 \times 0.0365 \times 2.9}} \div \frac{{{{\left( {12.12} \right)}^2} - {{\left( {8.12} \right)}^2}}}{{{{\left( {0.25} \right)}^2} + \left( {0.25} \right)\left( {19.99} \right)}}\) is:
The value of 4 ÷ 12 of [3 ÷ 4 of {(4 - 2) × 6 ÷ 2}] - 2 × 6 ÷ 8 + 3 is:
