Understanding the Square Root of 5

Result

√5 = 2.236068

Step-by-Step Process

Step 1: Find the Prime Factors of 5

5 is a prime number.

Since 5 is a prime number, the square root of 5 is already in its simplest form.

Properties of Square Root 5

  • Square: 5
  • Square Root: 2.236068
  • Number Type: Irrational
  • Perfect Square: No

Practical Applications

Geometry

If you have a square with an area of 5 square units, each side would measure √5 units.

Pythagorean Theorem

In a right triangle, if the hypotenuse measures 5 units, and one leg equals the other, each leg would measure √2.5 units.

Calculation Methods

Division Method

To approximate √5, you can use the division method:

  1. Take an approximate number (x)
  2. Divide 5 by x
  3. Average x with the result
  4. Repeat the process for greater accuracy

Frequently Asked Questions

What is the square root of 5?

The square root of 5 is 2.23606797749979, which is the number that, when multiplied by itself, gives 5.

Is 5 a prime number?

Yes, 5 is a prime number.

Is √5 a rational or irrational number?

√5 is an irrational number because it cannot be expressed as an exact fraction of two integers.

How to simplify √5?

Since 5 is a prime number, √5 is already in its simplest form.