Square Root Calculator
Calculate square roots, cube roots, and nth roots with step-by-step solutions
Square Root
√x or x^(1/2)
√x
Find the number that when multiplied by itself equals x
Result:
0
Cube Root
∛x or x^(1/3)
∛x
Find the number that when cubed equals x
Result:
0
nth Root
ⁿ√x or x^(1/n)
ⁿ√x
Calculate any root of x
Result:
0
Perfect Square Checker
Check if number is a perfect square
x = n²
Is x the square of an integer?
Result:
-
Square Number
x² - Inverse of square root
x²
Multiply number by itself
Result:
0
Power/Exponent
xⁿ - Raise to any power
xⁿ
Calculate x raised to power n
Result:
0
Understanding Roots & Powers
What is a Square Root?
The square root of a number x is a value that, when multiplied by itself, gives x.
Example:
√16 = 4 because 4 × 4 = 16
√25 = 5 because 5 × 5 = 25
√2 ≈ 1.414... (irrational number)
√16 = 4 because 4 × 4 = 16
√25 = 5 because 5 × 5 = 25
√2 ≈ 1.414... (irrational number)
Cube Roots & nth Roots
Cube Root: ∛27 = 3 because 3³ = 27
Fourth Root: ∜16 = 2 because 2⁴ = 16
Fifth Root: ⁵√32 = 2 because 2⁵ = 32
Fourth Root: ∜16 = 2 because 2⁴ = 16
Fifth Root: ⁵√32 = 2 because 2⁵ = 32
Properties of Roots
- √(a × b) = √a × √b
- √(a ÷ b) = √a ÷ √b
- (√a)² = a
- ⁿ√x = x^(1/n)
Perfect Squares (1-100)
Numbers that are squares of integers:
1
1²
4
2²
9
3²
16
4²
25
5²
36
6²
49
7²
64
8²
81
9²
100
10²
Common Applications
- Geometry and area calculations
- Pythagorean theorem
- Standard deviation in statistics
- Physics equations (velocity, energy)
- Engineering calculations
- Computer graphics & 3D modeling
- Financial calculations (compound interest)
- Distance and navigation
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