What's the square root of 387

General
1

what’s the square root of 387

2

What’s the square root of 387?

Answer: The square root of 387 is not an integer, as 387 is not a perfect square. Therefore, we need to find the square root using a method to approximate its value.

Calculation:

To get an approximation:

  • Use a calculator, or
  • Perform manual estimation.

Step-by-Step Estimation:

  1. Initial Estimate: Find two perfect squares between which 387 lies. These are 361 (19^2) and 400 (20^2). So, \sqrt{387} will be between 19 and 20.
  2. Interpolation:
    • Let’s pinpoint closer. Calculate 19.5^2 = 380.25. Since 380.25 < 387, \sqrt{387} > 19.5.
    • Calculate 19.6^2 = 384.16. Since 384.16 < 387, \sqrt{387} > 19.6.
    • Calculate 19.7^2 = 388.09. Since 388.09 > 387, \sqrt{387} < 19.7.

Thus, \sqrt{387} is approximately between 19.6 and 19.7.

For more precision, use a calculator:

\sqrt{387} \approx 19.6723

Conclusion: The square root of 387 is approximately 19.6723.