Understanding the Square Root of 135

Result

√135 = 11.618950

Step-by-Step Process

Step 1: Find the Prime Factors of 135

The prime factors of 135 are: 3, 3, 3, 5

Properties of Square Root 135

  • Square: 135
  • Square Root: 11.618950
  • Number Type: Irrational
  • Perfect Square: No

Practical Applications

Geometry

If you have a square with an area of 135 square units, each side would measure √135 units.

Pythagorean Theorem

In a right triangle, if the hypotenuse measures 135 units, and one leg equals the other, each leg would measure √67.5 units.

Calculation Methods

Division Method

To approximate √135, you can use the division method:

  1. Take an approximate number (x)
  2. Divide 135 by x
  3. Average x with the result
  4. Repeat the process for greater accuracy

Frequently Asked Questions

What is the square root of 135?

The square root of 135 is 11.61895003862225, which is the number that, when multiplied by itself, gives 135.

Is 135 a prime number?

No, 135 is not a prime number.

Is √135 a rational or irrational number?

√135 is an irrational number because it cannot be expressed as an exact fraction of two integers.

How to simplify √135?

To simplify √135, we look for the largest perfect square that divides 135 and take it out of the root.