Square Root Calculator
Calculate the square root of any number with step-by-step working. Recognises perfect squares, simplifies surds (e.g. √72 = 6√2), and gives decimal results for non-perfect squares.
√72
8.4853
How it works
Set up the square root
The square root of 72 is the number which, when multiplied by itself, equals 72.
Simplify the surd
72 = 6² × 2. So √72 = 6√2.
Decimal approximation
72 is not a perfect square, so √72 is an irrational number. To 6 decimal places: 8.485281.
Result:8.485281
The formula
Example substitution
Find the largest perfect square factor: 36. √72 = √36 × √2 = 6√2.
Worked examples
Find the square root of 144.
- 1Perfect square?: 12 × 12 = 144 ✓
- 2Result: √144 = 12 (exact)
Find and simplify √50.
- 1Largest sq factor: 25 (25 × 2 = 50)
- 2Simplify: √50 = √25 × √2 = 5√2
Find and simplify √200.
- 1Largest sq factor: 100 (100 × 2 = 200)
- 2Simplify: √200 = √100 × √2 = 10√2
Frequently asked questions
What is a square root?+
The square root of a number n is the value that, when multiplied by itself, gives n. Written as √n.
What is √144?+
√144 = 12, because 12 × 12 = 144.
What is √2 as a decimal?+
√2 ≈ 1.41421356... It is an irrational number — it cannot be expressed as a fraction.
What are perfect squares?+
Numbers whose square roots are whole numbers: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100...