Radical Calculator - Simplify Nth Roots Step by Step

Your details

The number multiplied in front of the radical sign. Use 1 if there is no coefficient.
The index tells you which root to take. 2 = square root, 3 = cube root, etc.
The number inside the radical sign. Must be positive for even-index roots. Negative values are allowed for odd-index roots.
Decimal valueSimplified form
8.48528137

Numeric approximation of the full expression

Simplified radical6*sqrt(2)
Factor outside radical6
Remaining radicand2
Exact integer resultNo - radical remains in simplified form
Prime factorization2^3 * 3^2
Factor outside radical6
Remaining radicand2

Simplified form: 6*sqrt(2)

  • You are computing the square root of 72.
  • After prime factorization, a factor of 6 comes outside the radical, leaving 2 inside.
  • The simplified form 6*sqrt(2) cannot be reduced further because 2 has no perfect square factors.
  • The decimal approximation is 8.485281.

Next stepTo verify: raise the simplified decimal to the power of 2 and check it equals the original radicand.

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