How to Calculate Square Root
What is Square Root?
The square root of a number x is a value r such that r² = x. Every positive number has two square roots: a positive (principal) root and a negative root. Only zero has a single square root: zero itself.
Step-by-Step Guide
- 1Factor the number into prime factors
- 2Pair up identical prime factors
- 3Take one factor from each pair and multiply them
- 4Any unpaired factors stay inside the radical symbol
Worked Examples
Input
√144
Result
12
12 × 12 = 144
Input
√2
Result
1.41421…
Irrational — cannot be simplified further
Input
√0.25
Result
0.5
0.5 × 0.5 = 0.25
Input
√200
Result
10√2
√(100 × 2) = 10√2 ≈ 14.142
Ready to calculate? Try the free Square Root Calculator
Try it yourself →