Question

The cube root $\sqrt[3]{{0.008}}$ is-
A. 0.2
B. 0.4
C. 0.002
D. None of these

Answer 1

Hint: The knowledge of cubes and cube roots will be required to solve this question. The cube root of a given number is a number which when multiplied by itself thrice gives back the given number. We will first write this number in the power of ten notation, and then factorize it. We then need to form triplets of the factors inside the cube root, so that the cube root sign can be eliminated, which will give us the required answer.

Complete step-by-step answer:

The given number whose cube root we need to calculate is 0.008. We will first convert this number in terms of power of ten, which has a general form as follows-
$A \times {10^b}$, where A is any number between 1 and 10, and b is an integer.

In order to write 0.008 in this notation, we need to move the decimal 3 places to the right, which can be done by multiplying and dividing the number by 1000 as-
$0.008 = 0.008 \times \dfrac{{1000}}{{1000}} = 8 \times \dfrac{1}{{1000}} = 8 \times \dfrac{1}{{{{10}^3}}} = 8 \times {10^{ - 3}}$
We also know that 8 is a cube of the number 2, so the number can further be factorized as-
$0.008 = 8 \times {10^{ - 3}} = {2^3} \times {10^{ - 3}}$
Now, this number has been factored, so we will try to find the cube root of the number by forming the triplets of these factors. This can be done as-
$\sqrt[3]{{0.008}} = \sqrt[3]{{{2^3} \times {{10}^{ - 3}}}} = \sqrt[3]{{\left( {\mathop {\underline {2 \times 2 \times 2} }\limits_{triplet} } \right) \times \left( {\mathop {\underline {{{10}^{ - 1}} \times {{10}^{ - 1}} \times {{10}^{ - 1}}} }\limits_{triplet} } \right)}}$
The cube root can now be eliminated because of these triplets. Only one factor in each triplet will be considered after the elimination of the triplet. So, the cube root of the given number can be written as-
$\sqrt[3]{{0.008}} = 2 \times {10^{ - 1}} = \dfrac{2}{{10}} = 0.2$
This is the required answer, and the correct option is A.

Note: Initially, it may seem that option C may be correct. This is because it seems intuitive that the cube root will have the same number of decimal places, so many students often mark the option as C, which is 0.002. These kinds of errors must be avoided. Also, some students may start calculating the square root when they are in a hurry.