Understanding the Square Root of 125

Result

√125 = 11.180340

Step-by-Step Process

Step 1: Find the Prime Factors of 125

The prime factors of 125 are: 5, 5, 5

Properties of Square Root 125

  • Square: 125
  • Square Root: 11.180340
  • Number Type: Irrational
  • Perfect Square: No

Practical Applications

Geometry

If you have a square with an area of 125 square units, each side would measure √125 units.

Pythagorean Theorem

In a right triangle, if the hypotenuse measures 125 units, and one leg equals the other, each leg would measure √62.5 units.

Calculation Methods

Division Method

To approximate √125, you can use the division method:

  1. Take an approximate number (x)
  2. Divide 125 by x
  3. Average x with the result
  4. Repeat the process for greater accuracy

Frequently Asked Questions

What is the square root of 125?

The square root of 125 is 11.180339887498949, which is the number that, when multiplied by itself, gives 125.

Is 125 a prime number?

No, 125 is not a prime number.

Is √125 a rational or irrational number?

√125 is an irrational number because it cannot be expressed as an exact fraction of two integers.

How to simplify √125?

To simplify √125, we look for the largest perfect square that divides 125 and take it out of the root.