Square Root Calculator
Calculate √x instantly
Example: 64, 2, 50, 144
How to Find Square Roots
For Perfect Squares
Memorize common perfect squares: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144...
For Non-Perfect Squares
1. Estimation Method:
√50 is between √49 (7) and √64 (8), closer to 7
2. Prime Factorization:
√72 = √(36 × 2) = 6√2
3. Calculator Method:
Examples
Example 1: √16
16 is a perfect square
4 × 4 = 16
Answer: 4
Example 2: √50
50 = 25 × 2
√50 = √(25 × 2) = √25 × √2 = 5√2
Answer: 5√2 ≈ 7.071
Example 3: √0.25
0.25 = 1/4
√(1/4) = √1/√4 = 1/2
Answer: 0.5
About Square Roots
A square root of a number is a value that, when multiplied by itself, gives the original number. The symbol √ is called a radical sign. Every positive number has two square roots (positive and negative), but we typically refer to the principal (positive) square root.
Perfect Squares
A perfect square is a number whose square root is a whole number. The first 12 perfect squares are: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144.
Properties of Square Roots
- √(a × b) = √a × √b
- √(a / b) = √a / √b
- √(a²) = |a|
- √0 = 0
- √1 = 1
Real-World Applications
- Geometry: Find side length from area (square with area 64 has side √64 = 8)
- Physics: Calculate velocity, energy, wave frequencies
- Finance: Compute standard deviation and risk metrics
- Engineering: Design calculations, signal processing
- Statistics: Standard deviation calculations
How to Use This Calculator
Enter a Number
Type any non-negative number.
Get Square Root
See square root, simplified radical, and if it's a perfect square.
Frequently Asked Questions
Can you take the square root of a negative number?
In real numbers, no. The square root of a negative number is imaginary (involves i, where i² = -1). For example, √(-1) = i.
What is the square root of 0?
The square root of 0 is 0, because 0 × 0 = 0.
Why are there two square roots?
Both +4 and -4 squared equal 16, so 16 has two square roots: ±4. However, the radical symbol √ refers only to the principal (positive) root.
How do I simplify √72?
Find the largest perfect square factor: 72 = 36 × 2. So √72 = √36 × √2 = 6√2.
What is the difference between √4 and 4²?
√4 = 2 (square root), while 4² = 16 (squaring). They are inverse operations.