Understanding the Square Root of 138

Result

√138 = 11.747340

Step-by-Step Process

Step 1: Find the Prime Factors of 138

The prime factors of 138 are: 2, 3, 23

Properties of Square Root 138

  • Square: 138
  • Square Root: 11.747340
  • Number Type: Irrational
  • Perfect Square: No

Practical Applications

Geometry

If you have a square with an area of 138 square units, each side would measure √138 units.

Pythagorean Theorem

In a right triangle, if the hypotenuse measures 138 units, and one leg equals the other, each leg would measure √69.0 units.

Calculation Methods

Division Method

To approximate √138, you can use the division method:

  1. Take an approximate number (x)
  2. Divide 138 by x
  3. Average x with the result
  4. Repeat the process for greater accuracy

Frequently Asked Questions

What is the square root of 138?

The square root of 138 is 11.74734012447073, which is the number that, when multiplied by itself, gives 138.

Is 138 a prime number?

No, 138 is not a prime number.

Is √138 a rational or irrational number?

√138 is an irrational number because it cannot be expressed as an exact fraction of two integers.

How to simplify √138?

To simplify √138, we look for the largest perfect square that divides 138 and take it out of the root.