Understanding the Square Root of 2

Result

√2 = 1.414214

Step-by-Step Process

Step 1: Find the Prime Factors of 2

2 is a prime number.

Since 2 is a prime number, the square root of 2 is already in its simplest form.

Properties of Square Root 2

  • Square: 2
  • Square Root: 1.414214
  • Number Type: Irrational
  • Perfect Square: No

Practical Applications

Geometry

If you have a square with an area of 2 square units, each side would measure √2 units.

Pythagorean Theorem

In a right triangle, if the hypotenuse measures 2 units, and one leg equals the other, each leg would measure √1.0 units.

Calculation Methods

Division Method

To approximate √2, you can use the division method:

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

Frequently Asked Questions

What is the square root of 2?

The square root of 2 is 1.4142135623730951, which is the number that, when multiplied by itself, gives 2.

Is 2 a prime number?

Yes, 2 is a prime number.

Is √2 a rational or irrational number?

√2 is an irrational number because it cannot be expressed as an exact fraction of two integers.

How to simplify √2?

Since 2 is a prime number, √2 is already in its simplest form.