Solve each equation Cubic squareroot 4m122 no solution 634 2

Solve each equation. Cubic squareroot 4m+1-2-2 no solution 63/4 27/4 11/4

Solution

³(4m +1) -2 = 2

==> ³(4m +1) = 2 + 2

==> (4m +1)^1/3 = 4         since ⁿx = x^1/n

Cubing on both sides

==> [(4m +1)^1/3]³ = 4³

==> (4m + 1)^{(1/3) *3} = 64        since (a^m)ⁿ = a^mn

==> (4m + 1) = 64

==> 4m = 64 - 1

==> 4m = 63

==> m = 63/4

Hence solution to ³(4m +1) -2 = 2 is m = 63/4

Option B