Understanding the Square Root of 8

Result

√8 = 2.828427

Step-by-Step Process

Step 1: Find the Prime Factors of 8

The prime factors of 8 are: 2, 2, 2

Properties of Square Root 8

  • Square: 8
  • Square Root: 2.828427
  • Number Type: Irrational
  • Perfect Square: No

Practical Applications

Geometry

If you have a square with an area of 8 square units, each side would measure √8 units.

Pythagorean Theorem

In a right triangle, if the hypotenuse measures 8 units, and one leg equals the other, each leg would measure √4.0 units.

Calculation Methods

Division Method

To approximate √8, you can use the division method:

  1. Take an approximate number (x)
  2. Divide 8 by x
  3. Average x with the result
  4. Repeat the process for greater accuracy

Frequently Asked Questions

What is the square root of 8?

The square root of 8 is 2.8284271247461903, which is the number that, when multiplied by itself, gives 8.

Is 8 a prime number?

No, 8 is not a prime number.

Is √8 a rational or irrational number?

√8 is an irrational number because it cannot be expressed as an exact fraction of two integers.

How to simplify √8?

To simplify √8, we look for the largest perfect square that divides 8 and take it out of the root.