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 300 in radical form
We will find the square root of 300 by prime factorisation method
The prime factorisation of 300 can be written as:
Step 1: Find the prime factors of 300
300÷ 2 = 150
150 ÷ 2 = 75
75 ÷ 5 = 15
15 ÷ 5 = 3
3 ÷ 3 = 1
300 = 2 X 2 X 5 X 5 X 3
Step 2: Pairing the factors
300 = (2×2)x(5×5)x3
√300 = √ (2×2)x(5×5)x3
√300 = 2 x 5 √3
√300=10√3
Answer
Hence, the square root of 300 = √300=10√3
