Square Root Calculator
Calculate square roots with high precision and simplify perfect-square radicals automatically.
Square Root Calculator
Calculate square roots with high precision and simplify perfect-square radicals automatically.
How to use the Square Root Calculator
- Enter a non-negative number.
- Click Calculate.
Formula
√n where n ≥ 0
Simplified radical: n = k² × r → √n = k√r
Example
√200 = √(100 × 2) = 10√2 ≈ 14.142136
Step-by-step calculation
- Find the largest perfect square factor of 200: 100.
- Extract: √200 = √100 × √2 = 10√2.
- Decimal: 10 × 1.4142136 = 14.142136.
Real-world uses
- Pythagorean theorem calculations.
- Standard deviation in statistics.
- Geometry and distance calculations.
Common mistakes
- Entering a negative number (square roots of negatives are not real numbers).
- Confusing square root with division by 2.
- Assuming √(a+b) = √a + √b (this is false).
Frequently asked questions
What is √2?
√2 ≈ 1.4142136. It is an irrational number with a non-repeating, infinite decimal expansion.
Can I find cube roots?
This calculator finds square roots. For cube roots, use the scientific calculator: n^(1/3).
Why does 9^(1/2) = 3?
A fractional exponent of 1/2 is equivalent to a square root. 9^(1/2) = √9 = 3.