To find the cube root of the fraction [tex]\(\frac{27}{1000}\)[/tex], follow these steps:
1. Understand the fraction: You need to take the cube root of [tex]\(\frac{27}{1000}\)[/tex].
2. Separate the numerator and denominator: Express the fraction as two separate parts under the cube root.
[tex]\[
\sqrt[3]{\frac{27}{1000}} = \frac{\sqrt[3]{27}}{\sqrt[3]{1000}}
\][/tex]
3. Find the cube root of the numerator: Calculate the cube root of 27.
[tex]\[
\sqrt[3]{27} = 3 \quad \text{(since } 3^3 = 27\text{)}
\][/tex]
4. Find the cube root of the denominator: Calculate the cube root of 1000.
[tex]\[
\sqrt[3]{1000} = 10 \quad \text{(since } 10^3 = 1000\text{)}
\][/tex]
5. Combine the results: Put the cube roots of the numerator and the denominator back into the fraction.
[tex]\[
\frac{\sqrt[3]{27}}{\sqrt[3]{1000}} = \frac{3}{10}
\][/tex]
6. Convert to decimal: Finally, convert [tex]\(\frac{3}{10}\)[/tex] to decimal form.
[tex]\[
\frac{3}{10} = 0.3
\][/tex]
Putting it all together, the cube root of [tex]\(\frac{27}{1000}\)[/tex] is:
[tex]\[
\sqrt[3]{\frac{27}{1000}} = 0.3
\][/tex]
So,
[tex]\[
\sqrt[3]{\frac{27}{1000}} = 0.30000000000000004
\][/tex]
(Note that the slight discrepancy from 0.3 is due to numerical precision in floating-point calculations.)
