Understanding the Square Root of 139

Result

√139 = 11.789826

Step-by-Step Process

Step 1: Find the Prime Factors of 139

139 is a prime number.

Since 139 is a prime number, the square root of 139 is already in its simplest form.

Properties of Square Root 139

  • Square: 139
  • Square Root: 11.789826
  • Number Type: Irrational
  • Perfect Square: No

Practical Applications

Geometry

If you have a square with an area of 139 square units, each side would measure √139 units.

Pythagorean Theorem

In a right triangle, if the hypotenuse measures 139 units, and one leg equals the other, each leg would measure √69.5 units.

Calculation Methods

Division Method

To approximate √139, you can use the division method:

  1. Take an approximate number (x)
  2. Divide 139 by x
  3. Average x with the result
  4. Repeat the process for greater accuracy

Frequently Asked Questions

What is the square root of 139?

The square root of 139 is 11.789826122551595, which is the number that, when multiplied by itself, gives 139.

Is 139 a prime number?

Yes, 139 is a prime number.

Is √139 a rational or irrational number?

√139 is an irrational number because it cannot be expressed as an exact fraction of two integers.

How to simplify √139?

Since 139 is a prime number, √139 is already in its simplest form.