Question

what is the value of (√x3) ^2/3 when x = 8 ​

Answer 1

This is your answer dear have a good day dear good morning ...

This is a problem involving an erroneous notation. The square root notation is used only for positive square root of a positive real number, and the above equation implies that √x = (2–8)/3=(-2), which in turn implies that x=(-2)^2 =4. But then √x be equal to 2, which leads to a contradiction. Even any complex value of x will not work, because if x=z=r(cos(t)+i.sin(t)) such that √x=√r(cos(t/2)+i.sin(t/2))=(-2), then √r =|-2|=2, cos(t/2)=(-1) and sin(t/2)=0, ==> t/2 = (2n+1)π ==> t=(4n+2)π ==> x=4(cos(t)+i.sin(t)) = 4 which again leads to √x=2, and not (-2). Hence there is no real or even complex solution.