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