Square Root Calculator
Calculate square roots with multiple methods
Input
Results
4.000000
Square Root
Using Newton's Method
Alternative Methods:
Built-in Math.sqrt:4.000000
Power Method:4.000000
Verification:
Result squared:16.000000
Original number:16
Understanding Square Roots
Definition
The square root of a number is a value that, when multiplied by itself, gives the number. For example, the square root of 16 is 4, because 4 × 4 = 16.
Properties
- • Every positive number has two square roots
- • The principal square root is positive
- • Perfect squares have whole number roots
- • Negative numbers have complex roots
Calculation Methods
Newton's Method
- • Iterative approximation
- • Fast convergence
- • High precision
- • Used in computers
Long Division
- • Traditional method
- • Step by step process
- • Good for learning
- • Works with paper
Prime Factorization
- • Works for perfect squares
- • Shows number structure
- • Simplifies radicals
- • Educational value