Answer:
[tex]\sqrt[3]{0.000004913}=0.017[/tex]
Step-by-step explanation:
Cubic Root
The cubic root of a number N is M, if
[tex]M^3=N[/tex]
It's usually tedious to manually compute cubic roots, but if we use some basic algebra concepts, the job is easily done.
Let's compute
[tex]M=\sqrt[3]{0.000004913}[/tex]
The argument can be expressed in scientific notation as
[tex]0.000004913= 4913\ 10^{-9}[/tex]
The power of 10 has an exact cubic root since the exponent is a multiple of 3. To find the cubic root of the mantissa, we note it's the triple product of 17, i.e.
[tex]4913=17*17*17=17^3[/tex]
Thus our number is
[tex]M=\sqrt[3]{17^3\ 10^{-9}}=17\ 10^{-3}=0.017[/tex]
We have then
[tex]\boxed{\sqrt[3]{0.000004913}=0.017}[/tex]
