cube root of 0.008
Understand the Problem
The question is asking to calculate the cube root of the number 0.008. To solve this, we will find a number that, when multiplied by itself three times, equals 0.008.
Answer
The cube root of $0.008$ is $\frac{1}{5}$.
Answer for screen readers
The cube root of $0.008$ is $\frac{1}{5}$.
Steps to Solve
- Identify the cube root operation
To find the cube root of a number, we can use the notation $\sqrt[3]{x}$, which means finding a number $y$ such that $y^3 = x$.
- Set up the equation
We need to set up the equation based on the number we want to find the cube root of: $$ y^3 = 0.008 $$
- Rewrite the number in a fractional form
Recognizing that $0.008$ can be rewritten as a fraction helps: $$ 0.008 = \frac{8}{1000} $$
- Simplify the fraction
We can simplify $\frac{8}{1000}$: $$ \frac{8}{1000} = \frac{1}{125} $$
- Identify the base numbers
Now we can express this in terms of exponents: $$ 1 = 1^3 \quad \text{and} \quad 125 = 5^3 $$
Thus: $$ 0.008 = \left(\frac{1}{5}\right)^3 $$
- Find the cube root
Taking the cube root of both sides: $$ y = \sqrt[3]{\left(\frac{1}{5}\right)^3} $$
By the property of cube roots, we have: $$ y = \frac{1}{5} $$
The cube root of $0.008$ is $\frac{1}{5}$.
More Information
The cube root of a number is the value that, when multiplied by itself three times, gives the original number. In this case, $\left(\frac{1}{5}\right)^3$ equals $0.008$.
Tips
- Forgetting that the cube root can be positive or negative; however, since $0.008$ is positive, we only take the positive root for this context.
- Miscalculating the fractions or not simplifying properly before attempting to find the cube root.
