Understanding the Square Root of 33
Result
Step-by-Step Process
Step 1: Find the Prime Factors of 33
The prime factors of 33 are: 3, 11
Properties of Square Root 33
- Square: 33
- Square Root: 5.744563
- Number Type: Irrational
- Perfect Square: No
Practical Applications
Geometry
If you have a square with an area of 33 square units, each side would measure √33 units.
Pythagorean Theorem
In a right triangle, if the hypotenuse measures 33 units, and one leg equals the other, each leg would measure √16.5 units.
Calculation Methods
Division Method
To approximate √33, you can use the division method:
- Take an approximate number (x)
- Divide 33 by x
- Average x with the result
- Repeat the process for greater accuracy
Frequently Asked Questions
What is the square root of 33?
The square root of 33 is 5.744562646538029, which is the number that, when multiplied by itself, gives 33.
Is 33 a prime number?
No, 33 is not a prime number.
Is √33 a rational or irrational number?
√33 is an irrational number because it cannot be expressed as an exact fraction of two integers.
How to simplify √33?
To simplify √33, we look for the largest perfect square that divides 33 and take it out of the root.