How do you find the square root of 1728?

To find the square root of 1728, you can use a few different methods. Here’s a straightforward approach:

Using Prime Factorization

First, break down 1728 into its prime factors:

• 1728 = 2 × 864
• 864 = 2 × 432
• 432 = 2 × 216
• 216 = 2 × 108
• 108 = 2 × 54
• 54 = 2 × 27
• 27 = 3 × 9
• 9 = 3 × 3

So, the prime factorization of 1728 is:

1728 = 2⁶ × 3³

Calculating the Square Root

To find the square root, take half the powers of the prime factors:

• For 2⁶, half is 2³ (which is 8).
• For 3³, half is 3^1.5 (which is 3√3).

Thus, the square root of 1728 is:

√1728 = 8 × 3√3 = 24√3

Using a Calculator

If you prefer a quicker method, simply use a calculator:

• Input 1728.
• Press the square root function.

This will give you approximately 41.57.

Conclusion

So, the square root of 1728 can be expressed as 24√3 or approximately 41.57 when calculated directly.