Question

The number of zeros in the cube root of 1000 is
A. 1
B. 2
C. 3
D. 4

Answer 1

Hint: In order to solve this question first we have to find out the cube root of 1000 then only we can comment on the zero digits of the cube root. So try to find out the cube root of 1000.

Complete step-by-step answer:
Given that find out the cube root of 1000
So as we know the cube root of a number x is written as $\sqrt[3]{{1000}}$
Here we have x = 1000
So cube root of 1000 would be $\sqrt[3]{{1000}}$
As we can write 1000 in factor of $10 = 10 \times 10 \times 10$
By putting it we get
$\sqrt[3]{{10 \times 10 \times 10}}$
Further solving it we get
$
   = \sqrt[3]{{{{\left( {10} \right)}^3}}} \\
   = {\left( {{{10}^3}} \right)^{\dfrac{1}{3}}} \\
   = 10 \\
 $
So the cube root of 1000 is 10
Since, there is 1 zero digit in 10 .

So, the correct answer is “Option A”.

Additional Information: The volume of a geometric cube is the cube, which gives rise to the name of its side length. The inverse operation is called extracting the cube root of n, which consists of finding a number whose cube is n. The side of the cube for a given volume is determined. N is therefore elevated to the power of one-third.

Note: For finding the cube root of a number means finding the numbers power of one third that can be written as if we take number as x so the cube root will be $\sqrt[3]{x}$ and we can write it also as ${x^{\dfrac{1}{3}}}$ .