Definition – What is a root?

A root is a number that is multiplied by itself the root number of times.

• Square root (root 2) of 16: √16 = 4, because 4 × 4 = 16
• Cube root (root 3) of 27: ³√27 = 3, because 3 × 3 × 3 = 27
• Fourth root of 4,096: ⁴√4096 = 8, because 8 × 8 × 8 × 8 = 4096
• Fifth root of 32,768: ⁵√32768 = 8, because 8 × 8 × 8 × 8 × 8 = 32768
• Decimal roots are also possible, e.g., 2.5th root of 70: 2.5√70 ≈ 5.470652

Formula – How to calculate a root

The nth root of a number x can be calculated using:

nth root of x = x^(1/n) = exp(ln(x)/n)

Example – Find the fifth root of 55

Using the formula:

5√55 = exp(ln(55)/5) ≈ 2.2288073840