nth roots and rational powers
Learn nth roots through powers: even and odd roots, multiplying roots, then fractional powers like 2713 and 823.
- Germany: grade 9
- Iran: grade 10
- Palestine: grade 9
- Ukraine: grade 10
- Russia: grade 10
Guide
This studio follows Iran Grade 10 Math 1, chapter 3 (nth roots and rational powers).
b is an nth root of a when bⁿ = a. For example 3 is a fourth root of 81 because 34 = 81.
For an even n a positive number has two nth roots (3 and −3 for 81) and a negative number has none. For an odd n every number has exactly one nth root, with the same sign.
Product rule: ⁿ√a × ⁿ√b = ⁿ√(ab) for a, b not negative.
Rational powers: a1n means ⁿ√a, and amn means (ⁿ√a)ᵐ.