Understanding the Square Root of 119

Result

√119 = 10.908712

Step-by-Step Process

Step 1: Find the Prime Factors of 119

The prime factors of 119 are: 7, 17

Properties of Square Root 119

  • Square: 119
  • Square Root: 10.908712
  • Number Type: Irrational
  • Perfect Square: No

Practical Applications

Geometry

If you have a square with an area of 119 square units, each side would measure √119 units.

Pythagorean Theorem

In a right triangle, if the hypotenuse measures 119 units, and one leg equals the other, each leg would measure √59.5 units.

Calculation Methods

Division Method

To approximate √119, you can use the division method:

  1. Take an approximate number (x)
  2. Divide 119 by x
  3. Average x with the result
  4. Repeat the process for greater accuracy

Frequently Asked Questions

What is the square root of 119?

The square root of 119 is 10.908712114635714, which is the number that, when multiplied by itself, gives 119.

Is 119 a prime number?

No, 119 is not a prime number.

Is √119 a rational or irrational number?

√119 is an irrational number because it cannot be expressed as an exact fraction of two integers.

How to simplify √119?

To simplify √119, we look for the largest perfect square that divides 119 and take it out of the root.