Question

If `sqrt(x-1)=2`, what is `(x - 1)^2` ?

Answer 1

`(x-1)^2=16`

Explanation:

Square both sides:

`(sqrt(x-1))^2=(2)^2`

This causes the radical to cancel out:

`(x-1)=4`

Square both sides, again:

`(x-1)^2=4^2`

`(x-1)^2=16`

Answer 2

`(x-1)^2=16`

Explanation:

`color(blue)"square both sides"`

`"note that "sqrtaxxsqrta=(sqrta)^2=a`

`rArr(sqrt(x-1))^2=2^2`

`rArrx-1=4`

`color(blue)"square both sides"`

`(x-1)^2=4^2`

`rArr(x-1)^2=16`