Question

What is `x` in the equation `1000 = (x - 8) ^(3/2)`?

Answer 1

`x=108`

Explanation:

`1000=(x-8)^(3/2)`

Cube root both sides

`10=(x-8)^(1/2)`

Square both sides

`100=x-8`

Add 8

`x=108`

Answer 2

`x=108`

Explanation:

`(x-8)^(3/2)=1000`

`(x-8)^(3/2)=10^3`

`(x-8)^3=10^6`

`x-8=10^2`

`x=10^2+8=108`

Answer 3

`x=108`

Explanation:

Note that `1000 = 10^3`

Raise both sides to the power of `2/3`

`(10^3)^(2/3) = ((x-8)^(3/2))^(2/3)`

Multiply the indices:

`10^2 =x-8`

`100 =x-8`

`108=x`

Answer 4

`color(maroon)(x = 108`

Explanation:

`1000 = (x-8)^(3/2)`

`10^3 = (x - 8)^(3/2)`

`(100^(1/2))^3 = (x - 8)^(3/2)`

`100^(3/2) = (x - 8)^(3/2)`

`100 = x - 8`

`color(maroon)(x = 108`