Result
Step-by-Step Solution
📚 Calculation History
Track your recent calculations
📚 How to Use the Square Root Calculator
Master square root calculations with our comprehensive guide
Basic Input
Enter expressions using the √ symbol or sqrt() function. Examples: √16, sqrt(25), or 2√3
Complex Expressions
Combine multiple terms with + and - operators: √12 + √27 - √3
Quick Buttons
Use the quick input buttons for common square roots and operators
Step-by-Step
View detailed solutions showing simplification and combination of like terms
🧮 Square Root Fundamentals
Understanding the mathematics behind square roots
Perfect Squares
Numbers that are squares of integers:
- √1 = 1
- √4 = 2
- √9 = 3
- √16 = 4
- √25 = 5
Simplification
Breaking down complex square roots:
- √12 = √(4×3) = 2√3
- √18 = √(9×2) = 3√2
- √50 = √(25×2) = 5√2
Like Terms
Combining similar square roots:
- 2√3 + 5√3 = 7√3
- √2 + 3√2 = 4√2
- √5 - 2√5 = -√5
💡 Practical Examples
Real-world applications and sample calculations
Geometry Applications
Pythagorean Theorem:
Finding the hypotenuse of a right triangle with legs 3 and 4:
√(3² + 4²) = √(9 + 16) = √25 = 5
Distance Formula
Between two points:
Distance between (1,2) and (4,6):
√((4-1)² + (6-2)²) = √(9 + 16) = √25 = 5
Algebraic Expressions
Simplifying radicals:
√72 + √32 - √18
= 6√2 + 4√2 - 3√2 = 7√2
🎯 Pro Tips & Shortcuts
Advanced techniques for efficient calculations
Quick Recognition
Memorize perfect squares up to 25² = 625 for faster mental calculations
Prime Factorization
Break numbers into prime factors to identify perfect square factors easily
Estimation
Use nearby perfect squares to estimate: √50 is between √49=7 and √64=8
Rationalization
Multiply by conjugates to eliminate square roots from denominators
🎯 Calculator Features
Everything you need for square root calculations
Auto Simplification
Automatically reduces √12 to 2√3 and combines like terms
Step-by-Step Solutions
See detailed breakdown of every calculation process
Mixed Number Support
Handle expressions like 2√3 + 5√2 with ease
Addition & Subtraction
Perform complex operations with multiple square roots
Decimal Approximations
Toggle between exact and decimal representations
Copy Results
One-click copying to clipboard for easy sharing
