Question

Can someone explain how to solve this: b ^ 3/2 = 8

Answer 1

square both sides then cbrt it ....

Answer 2

b^3/2=8
b=8^2/3
b=2

Answer 3

sorry b=4

Answer 4

When having b ^ 2 = 4 where the solution is b = ± 2 why can't we exponentiate both sides to the 1/2 ?

Answer 5

we can... but this is the easier method

Answer 6

If you do you ll get b = 4 ^ 1/2 which equals 2 not -2 .. No ?

Answer 7

quadratics do not have an inverse unless you restrict the domain

Answer 8

So, why is it correct to do so when having b ^ 3/2 = 8 ?

Answer 9

you are squaring, squaring is a function such that for any given input there is only 1 result. trying to undo the square is not a function in that for any given input other than 0, there are 2 possible solutions.

Answer 10

(-2)^2 = 4

(2)^2 = 4

each input has only 1 solution. but we cannot say that sqrt(4) has only 1 solution unless we restrict the domain.

Answer 11

substitute the values into the equation and you'll get one answer

Answer 12

Hmm... if understood correctly when having b ^ 3/2 = 8 <=> b ^ 3 = 8 ^ 2.
But then why it can be b = 3rd root of 8 ^ 2 and not - 3rd root of 8 ^ 2

Answer 13

cbrt is a function with an inverse

Answer 14

there are no 2 input to b^3 that give the same value. therefore we can cbrt any number and get a unique result

Answer 15

Thnx

Answer 16

youre welcome