Find the square root of 1728 in radical form

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

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