nth roots and rational powers
Learn nth roots through powers: even and odd roots, multiplying roots, then fractional powers like ٢٧١٣ and ٨٢٣.
- فلسطين: الصف ٩
- إيران: الصف ١٠
- أوكرانيا: الصف ١٠
- روسيا: الصف ١٠
- ألمانيا: الصف ٩
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الدليل
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 ٣٤ = ٨١.
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: a١n means ⁿ√a, and amn means (ⁿ√a)ᵐ.