Question

The cube root of 0.000004913 is

Answer 1

Answer:

$\sqrt[3]{0.000004913}=0.017$

Step-by-step explanation:

Cubic Root

The cubic root of a number N is M, if

$M^3=N$

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

$M=\sqrt[3]{0.000004913}$

The argument can be expressed in scientific notation as

$0.000004913= 4913\ 10^{-9}$

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.

$4913=17*17*17=17^3$

Thus our number is

$M=\sqrt[3]{17^3\ 10^{-9}}=17\ 10^{-3}=0.017$

We have then

$\boxed{\sqrt[3]{0.000004913}=0.017}$