Understanding the Square Root of 3

Result

√3 = 1.732051

Step-by-Step Process

Step 1: Find the Prime Factors of 3

3 is a prime number.

Since 3 is a prime number, the square root of 3 is already in its simplest form.

Properties of Square Root 3

  • Square: 3
  • Square Root: 1.732051
  • Number Type: Irrational
  • Perfect Square: No

Practical Applications

Geometry

If you have a square with an area of 3 square units, each side would measure √3 units.

Pythagorean Theorem

In a right triangle, if the hypotenuse measures 3 units, and one leg equals the other, each leg would measure √1.5 units.

Calculation Methods

Division Method

To approximate √3, you can use the division method:

  1. Take an approximate number (x)
  2. Divide 3 by x
  3. Average x with the result
  4. Repeat the process for greater accuracy

Frequently Asked Questions

What is the square root of 3?

The square root of 3 is 1.7320508075688772, which is the number that, when multiplied by itself, gives 3.

Is 3 a prime number?

Yes, 3 is a prime number.

Is √3 a rational or irrational number?

√3 is an irrational number because it cannot be expressed as an exact fraction of two integers.

How to simplify √3?

Since 3 is a prime number, √3 is already in its simplest form.