Square root of a number is the value that returns the original number on multiplied by itself. Finding square root by prime factorisation is an easy method. We need to factories the number under the root and pair them in two.
Finding the square root of 52 in radical form
We will find the square root of 52 by prime factorisation method
The prime factorisation of 52 can be written as:
Step 1: The first step is to divide the number 52 with the smallest prime factor, say 2.
52 ÷ 2 = 26
Step 2: You will get a fractional number if you divide 26 by 2.
26 ÷ 2 = 13
Now 13 is a prime number
13 ÷ 13 = 1
Finally, we have received number 1 at the end of the division process. So that we cannot proceed further.
So, the prime factors of 52 are written as 2 X 2X 13
On paring we get
52 = (2×2) x 13
Square root of 52 = √52= √(2×2) x 13
= √52= 2√13
√52= 2√13
Answer
Hence, the square root of 52 = √52=2√13
