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 1728 in radical form
We will find the square root of 1728 by prime factorisation method
The prime factorisation of 1728 can be written as:
Step 1: Find the prime factors of 1728
1728÷ 2 = 864
864 ÷ 2 = 432
432 ÷ 2 = 216
216 ÷ 2 = 108
108 ÷ 2 = 54
54 ÷ 2 = 27
27 ÷ 3 = 9
9 ÷ 3 = 3
3 ÷ 3 = 1
1728 = 2x2x2x2x2x2x3x3x3
Step 2: Pairing the factors
1728 = (2×2)x(2×2)x(2×2)x(3×3)x3
√1728 = √ (2×2)x(2×2)x(2×2)x(3×3)x3
√1728 = 2 x 2 x 2 x 3 √3
√1728=24√3
Answer
Hence, the square root of 1728 = √1728=24√3
