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Square Root Calculator
Calculate square roots and perfect squares
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Math & Geometry ✅ Free to Use
Square Root Calculator
Calculate square roots, cube roots, nth roots, and perfect powers. Includes perfect square and cube detection with nearby values.
√16.000000
4.00000000
✅ Perfect Square
Calculation Details
Input Number: 16.000000
Result: 4.00000000
Rounded Result: 4.0000
Integer Part: 4
Verification: 4.0000² = 16.000000
Perfect Square: Yes
Decimal Places: 0
Perfect Squares Near 16
2² = 4
√4 = 2
3² = 9
√9 = 3
4² = 16
√16 = 4
5² = 25
√25 = 5
6² = 36
√36 = 6
Common Square and Cube Roots
Perfect Squares
√1 1
√4 2
√9 3
√16 4
√25 5
√36 6
√49 7
√64 8
√81 9
√100 10
√121 11
√144 12
Perfect Cubes
∛1 1
∛8 2
∛27 3
∛64 4
∛125 5
∛216 6
∛343 7
∛512 8
∛729 9
∛1000 10
Root Properties and Rules
Square Root Properties
√(a × b) = √a × √b
√(a ÷ b) = √a ÷ √b
√a² = |a|
√a × √a = a (for a ≥ 0)
Cube Root Properties
∛(a × b) = ∛a × ∛b
∛(a ÷ b) = ∛a ÷ ∛b
∛a³ = a
∛(-a) = -∛a
General Rules
ⁿ√(aᵐ) = a^(m/n)
ⁿ√a × ⁿ√b = ⁿ√(a × b)
(ⁿ√a)ⁿ = a
ⁿ√ᵐ√a = ⁿᵐ√a
Important Notes
• Even roots of negative numbers are undefined in real numbers
• Odd roots of negative numbers are negative
• √0 = 0 and ⁿ√0 = 0
• √1 = 1 and ⁿ√1 = 1