Question

Find the cube root of the following decimal numbers:
\[0.003375\]

Answer 1

Hint: Here we need to find the cube root of the given decimal number. For that, we will first write the decimal number as a fraction with numerator and denominator. Then we will find the cube root of the numerator and denominator using the factorization method. After getting the cube root of the numerator and denominator, we will again write the fraction as a decimal number.

Complete step-by-step answer:
Here we need to find the cube root of the decimal number \[0.003375\].
Now, we will first express the decimal number as the fraction with a numerator and denominator.
We can write \[0.003375\] as
\[0.003375 = \dfrac{{3375}}{{1000000}}\]
Now, we will find the cube root of the numerator and denominator using the factorization method.
We will first write the numerator and denominator as products of the factors.
We know that \[3375 = 5 \times 5 \times 5 \times 3 \times 3 \times 3\] and \[1000000 = 10 \times 10 \times 10 \times 10 \times 10 \times 10\]. Therefore,
\[ \Rightarrow 0.003375 = \dfrac{{5 \times 5 \times 5 \times 3 \times 3 \times 3}}{{1000000}}\]
Now, we will pick out the factors which have occurred 3 times in the numerator and denominator.
We can see that 5 and 3 has occurred 3 times in the numerator and 100 has 3 times in the denominator.
Therefore, the cube root of the decimal number \[0.003375\] is equal to
\[ \Rightarrow \sqrt[3]{{0.003375}} = \sqrt[3]{{\dfrac{{5 \times 5 \times 5 \times 3 \times 3 \times 3}}{{10 \times 10 \times 10 \times 10 \times 10 \times 10}}}} = \dfrac{{5 \times 3}}{{10 \times 10}}\]
Now, we will multiply the numbers in numerator and denominator.
\[ \Rightarrow \sqrt[3]{{0.003375}} = \dfrac{{15}}{{100}}\]
Now, we will again write this fraction as a decimal number.
\[ \Rightarrow \sqrt[3]{{0.003375}} = 0.15\]
Hence, the cube root of the decimal number \[0.003375\] is equal to \[0.15\].

Note: The number given to us is a decimal number. A decimal number is defined as a number whose decimal part and the whole number part is separated by a decimal point. The dot which is used in the decimal number is known as the decimal point. A decimal number can be converted to fraction and then back to decimal.