Roots
Roots reverse exponents. The nth root undoes raising to the nth power. Essential for CAGR.
Practice This ConceptUnderstanding Roots
A root is the inverse of an exponent. If 2 cubed = 8, then the cube root of 8 = 2. In EPSO, roots appear in CAGR — you need the nth root to extract the annual rate from multi-year data.
Formula
$\sqrt[n]{x} = x^{\frac{1}{n}}$
Key Rules
- Square root of x = x^(1/2)
- Cube root of x = x^(1/3)
- nth root of x = x^(1/n)
- The larger n, the closer result is to 1
Examples in Action
1
1.32^(1/4)
=
1.072
4th root = annual growth multiplier
2
sqrt(9)
=
3
Square root: 3 x 3 = 9
3
8^(1/3)
=
2
Cube root: 2 x 2 x 2 = 8
Common Errors
- Confusing nth root with dividing by n
- Wrong n (2018 to 2022 = 4 years, not 5)
- Forgetting to subtract 1 after root in CAGR
Pro Tip
On a calculator, the nth root = x^(1/n). For 4th root, raise to 0.25. For 5th root, raise to 0.2.