Square Root Calculator
Calculate the square root of any number
Square Root Calculator
How to Calculate the Square Root of a Number
What is a Square Root?
The square root of a number is a value that, when multiplied by itself, gives the original number. For example, the square root of 144 is 12, because 12 × 12 = 144. It is denoted by the symbol √ (radical).
Perfect Squares
A number is a perfect square if its square root is a whole number.
- √1 = 1, √4 = 2, √9 = 3, √16 = 4, √25 = 5
- √36 = 6, √49 = 7, √64 = 8, √81 = 9, √100 = 10
- √121 = 11, √144 = 12, √169 = 13, √196 = 14, √225 = 15
Calculation Methods
- Trial method — find a number whose square equals the given number
- Prime factorization — decompose the number into prime factors
- Newton's method — iterative algorithm for approximate calculation
Properties of Square Roots
- √(a × b) = √a × √b
- √(a / b) = √a / √b
- (√a)² = a
- √a² = |a|
Practical Applications
- Geometry — Pythagorean theorem, diagonal calculations
- Physics — velocity, acceleration, electrical quantities
- Statistics — standard deviation and variance
- Finance — volatility calculation, Black-Scholes model
Interesting fact: the square root of 2 (approximately 1.41421356...) was the first irrational number discovered by ancient Greeks. It cannot be expressed as a fraction.
See Also
- Factors of a Number - List all Factors and Factor Pairs of a Number
- Prime Number Checker - Find out whether a given number is Prime or not
- Prime Factorization - Prime Factorization Calculator
- Prime Numbers List - List of all Prime Numbers - how many Prime numbers are between
Square Root Calculator
This calculator will help you find the square root of any number. For example, it can help you find out what is the square root of 144? (The answer is: 12). Enter a number (e.g. '144') and hit the 'Calculate' button.
FAQ
What is a square root?
The square root of a number is the value that gives that number when multiplied by itself: √144 = 12, because 12 × 12 = 144.
What is a perfect square?
A number whose square root is a whole number: 1, 4, 9, 16, 25, 36 and so on. 144 is a perfect square (12²), while 7 is not — √7 = 2.6457513111, a decimal that never ends and never repeats.
Does every positive number have two square roots?
Yes: 12 × 12 = 144 and (−12) × (−12) = 144 as well. The radical sign √ stands for the non-negative root only, so √144 = 12 and the other root is written as −12. Negative numbers have no square root among the real numbers.