Understanding the Square Root of 123
Result
Step-by-Step Process
Step 1: Find the Prime Factors of 123
The prime factors of 123 are: 3, 41
Properties of Square Root 123
- Square: 123
- Square Root: 11.090537
- Number Type: Irrational
- Perfect Square: No
Practical Applications
Geometry
If you have a square with an area of 123 square units, each side would measure √123 units.
Pythagorean Theorem
In a right triangle, if the hypotenuse measures 123 units, and one leg equals the other, each leg would measure √61.5 units.
Calculation Methods
Division Method
To approximate √123, you can use the division method:
- Take an approximate number (x)
- Divide 123 by x
- Average x with the result
- Repeat the process for greater accuracy
Frequently Asked Questions
What is the square root of 123?
The square root of 123 is 11.090536506409418, which is the number that, when multiplied by itself, gives 123.
Is 123 a prime number?
No, 123 is not a prime number.
Is √123 a rational or irrational number?
√123 is an irrational number because it cannot be expressed as an exact fraction of two integers.
How to simplify √123?
To simplify √123, we look for the largest perfect square that divides 123 and take it out of the root.