Question

The cube root of $1.331$ is:
A) $0.11$
B) $0.011$
C) $11$
D) $1.1$

Answer 1

Hint:
For solving such types of questions we have to do prime factors of the given number. After that we have to take the cubic root on both sides and we also have to use the decimal property of the numbers to get the final answer.

Complete step by step solution:
Given number is
$a=1.331$
Now we have to use the prime factorization method to get the factors of the given number.
The prime factors of $1331$ are as follows:
$1331=11\times 11\times 11$
Now divide the LHS and RHS of the above equation with $1000$ we get
$\dfrac{1331}{1000}=\dfrac{11}{10}\times \dfrac{11}{10}\times \dfrac{11}{10}$
Further solving the above expression
$1.331=1.1\times 1.1\times 1.1$
The above expression can be written as
$1.331={{\left( 1.1 \right)}^{3}}$
Therefore, the cubic root of above expression is given by
$\sqrt[3]{1.331}=\sqrt[3]{{{\left( 1.1 \right)}^{3}}}$
By solving the above expression
$\sqrt[3]{1.331}=1.1$
Hence, the cubic root of $1.331$ is $1.1$

Therefore, option D is correct.

Additional information:
Prime factors of a number are the factors that are the multiplications of prime numbers. The prime numbers are the numbers that have only two factors first is themselves and other is $1$. For example the first five prime numbers are $2,3,5,7,11$. The only single even prime number is $2$ and other numbers are the odd prime numbers.

Note:
Since we have to find the cubic root of this first of all we have to know the factors of . After that it is also very important to take care of decimal for getting the right answer because if we place decimal at the wrong place the whole solution becomes wrong.