Question

Find the cube root of 1331.

Answer 1

Hint: To solve this question, the best way is to factorize the number and represent the number in terms of the product of prime numbers. As the number is very large this will help in solving the question very accurately. We keep on factorizing unless and until we get 1 at the last step by dividing by prime numbers.

Complete step-by-step answer:
Before solving this question, we must know about cube roots.
The cube root of a number is a special value that, when used in a multiplication three times, gives that number.
Example: \[2\times 2\times 2=8\] , so the cube root of 8 is 2.
\[3\times 3\times 3=27\] , so the cube root of 27 is 3.
Let us now know about the Prime Factorization method.
The method of prime factorization is used to ‘break down’ or express a given number as a product of prime numbers.
We will be using the prime factorization method to find the cube root of 1331. As explained above, we are going to break down the number 1331 as a product of prime numbers.
Then we will group the prime factors of 1331 in three in such a way that each number of groups is the same. Then we will take one factor from each group and will multiply them together to get the square root of 1331.
As mentioned in the hint, to find the cube root of any number, we need to do the prime factorization of that number.
In order to find the cube root of a number by prime factorization, we have to use the following steps:
Step1. Perform the prime factorization of the number.
Step2. Resolve it into prime factors.
Step3. Group the prime factors in three in such a way that each number of the group is the same.
Step4. Take one factor from each group.
Step5. Find the product of the factors obtained. This product is the required cube root.
Now, do the same steps with 1331 to find its square root.
\[\begin{align}
  & 11\overline{\left){1331}\right.} \\
 & \ 11\overline{\left){121}\right.} \\
 & \ \ 11\overline{\left){11}\right.} \\
 & \ \ \ \ \ \overline{\left){1}\right.} \\
\end{align}\]

1331 = \[11\times 11\times 11=11\] \[\]
\[{{\left( 11 \right)}^{3}}=1331\,\] , i.e. \[\left( 11\times 11\times 11 \right)=1331\]
So, the square root of 1331 is 11.

Note: We can also find the square root of a number by the method of Prime Factorization.
In order to find the square root of a number by prime factorization, we have to use the following steps:
Step1. Perform the prime factorization of the number.
Step2. Resolve it into prime factors.
Step3. Group the prime factors in two in such a way that each number of the group is the same.
Step4. Take one factor from each group.
Step5. Find the product of the factors obtained. This product is the required cube root.
So, this is how we can find the square root of any number. Also, try not to make any calculation mistakes.