Question

Find the square root of the following number by the prime factorization method.
1521.

Answer 1

Hint: To find the square root of the following number by prime factorization method, we will write 1521 as the multiple of primes. After writing in the form of primes, and will be written in the form of a group of two. Then, from groups, we will select one prime number and we will multiply all such prime numbers. The square root of 1521 will be the product of these prime numbers.

Complete step-by-step answer:
Before we solve the question above, we must first know 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. So, in this method, we will try to write 121 as the product of primes. So to find the product of primes, we will do prime factorization of 1521:

 

Thus, we can write 1521 as:
$1521=3\times 3\times 13\times 13$
Now, we will take the same prime numbers and we will write them in the group of two as shown below:
$1521=\left( 3\times 3 \right)\times \left( 13\times 13 \right)$
Now, we will take one number from each group. So, from first we will get 3 and from second group, we get 13. The square root of 1521 will be the product of these numbers. Thus, we will get:
$\begin{align}
  & \text{Square root of 1521=13}\times \text{13} \\
 & \Rightarrow \text{Square root of 1521=39} \\
 & \Rightarrow \sqrt{1521}=39. \\
\end{align}$

Note: When we have done grouping, we have made groups of two prime numbers because we have to find the square root of the given number. If we had to find the cube root of any number then we would have used it to calculate the square root is valid only when the given integer is a square number.