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
If P = 0.3 × 0.3 + 0.03 × 0.03 - 0.6 × 0.03 and Q = 0.54, then \(\rm \frac{P}{Q}\) is equal to:
The value of \(\left(\frac{1}{2}\right)^{−2} \times\left(\frac{1}{3}\right)^{−2} \times\left(\frac{1}{4}\right)^{−2} \) is
The solution of the equation \(\frac{2}{3 x-4}+\frac{2}{2 x-6}=0 \) is:
What will come in the place of question mark (?) in the given expression?
\(\sqrt{21+\sqrt{49}+\sqrt{64}} \space {\%\:of\:5000}=?\)
There are 5 tasks and 5 persons. Task-1 cannot be assigned to either person-1 or person-2. Task-2 must be assigned to either person-3 or person-4. Every person is to be assigned one task. In how many ways can the assignment be done?
