Question

Cube root of \[0.125\] is:
A.\[0.5\]
B.\[5\]
C.\[0.05\]
D.\[2.5\]

Answer 1

Hint: Here we have to find the cube root of a given number. Cube root is the factor that is multiplied three times by itself to get the required number. We can find the cube root of any decimal number by converting it to fraction and then finding all the factors using the prime factorization method.

Complete step-by-step answer:
We have to find cube root of \[0.125\] .
Now, we know that, the number \[0.125\], has a whole number part, i.e. those digits which are on the left hand side of the decimal place.
In the given question, whole number part is 0 .
Also, the given number has a fractional part , i.e. the digits which appear on the right hand side of the decimal part .
In the given question, the fractional part is 125 .
Now, we know that we can convert any decimal number in the form of a fraction having a numerator and denominator.
Hence, the given number can be written as:
\[0.125 = \dfrac{{125}}{{1000}}\]
Here, there were 3 digits after the decimal point, hence in the denominator we have considered 3 zeros.
Now, to find the cube root of the numerator and denominator, we will use the method of prime factorization.

So, \[1000 = 10 \times 10 \times 10\] and \[125 = 5 \times 5 \times 5\].
Now, the number can be written as:
\[ \Rightarrow 0.125 = \dfrac{{5 \times 5 \times 5}}{{10 \times 10 \times 10}}\]
Now, we have to find the cube root.
Taking cube root on both the side, we get
\[ \Rightarrow \sqrt[3]{{0.125}} = \sqrt[3]{{\dfrac{{5 \times 5 \times 5}}{{10 \times 10 \times 10}}}}\]
\[ \Rightarrow \sqrt[3]{{0.125}} = \dfrac{5}{{10}}\]
As \[\dfrac{1}{{10}}\] can be written as a decimal \[0.1\]. So we can rewrite above equation as:
\[\sqrt[3]{{0.125}} = 0.5\]
Hence, option A is the required answer.

Note: We have to find the cube root of a decimal number using prime factorization method. Prime factorization is a method of finding all the factors in terms of prime numbers. Prime numbers are the numbers which have only 2 factors that is 1 and itself. The only even prime number is 2.