Understanding the Square Root of 133

Result

√133 = 11.532563

Step-by-Step Process

Step 1: Find the Prime Factors of 133

The prime factors of 133 are: 7, 19

Properties of Square Root 133

  • Square: 133
  • Square Root: 11.532563
  • Number Type: Irrational
  • Perfect Square: No

Practical Applications

Geometry

If you have a square with an area of 133 square units, each side would measure √133 units.

Pythagorean Theorem

In a right triangle, if the hypotenuse measures 133 units, and one leg equals the other, each leg would measure √66.5 units.

Calculation Methods

Division Method

To approximate √133, you can use the division method:

  1. Take an approximate number (x)
  2. Divide 133 by x
  3. Average x with the result
  4. Repeat the process for greater accuracy

Frequently Asked Questions

What is the square root of 133?

The square root of 133 is 11.532562594670797, which is the number that, when multiplied by itself, gives 133.

Is 133 a prime number?

No, 133 is not a prime number.

Is √133 a rational or irrational number?

√133 is an irrational number because it cannot be expressed as an exact fraction of two integers.

How to simplify √133?

To simplify √133, we look for the largest perfect square that divides 133 and take it out of the root.