Root Calculator
Calculate square roots, cube roots, and nth roots, and simplify radicals.
Calculate root
√144
√144
12.000000
✓ Perfect root (integer)
Verification
12.0000002 = 144.000000
Verification
0,0000
Exponent form
0,0000
Root properties
Root of product
√(a × b) = √a × √b
Root of quotient
√(a / b) = √a / √b
Root of power
ⁿ√(aᵐ) = a^(m/n)
What is a root?
The nth root of a number is another number that when raised to n gives the original. √x = x^(1/2) answers: what number multiplied by itself gives x? It's the inverse of exponentiation.
Types of roots
Square root (√): index 2, the most common. Cube root (∛): index 3, accepts negatives. Even roots don't accept negative radicands in real numbers.
Radical simplification
Simplifying means extracting factors that are perfect powers. √72 = √(36×2) = 6√2. We look for perfect squares inside the radicand.