Arithmetic roots of powers with a natural exponent
Answers are for parents and teachers.
1
Compute ⁵√32 - ³√27 + √49.
6
2
Solve x³ = 125.
x = 5
3
Solve x⁶ = 64.
x = ±2
4
Find all x for which √(2x + 6) makes sense.
x ≥ -3
5
Why does x⁵ = -32 have one root but x⁴ = 16 two roots?
With an odd power the sign of the result matches the sign of x, so x = -2 is the only root. With an even power x and -x give the same result, so both 2 and -2 work.