Question

How do you solve `(y - 8) ^ { 2} = 49`?

Answer 1

`y=1" or " y=15`

Explanation:

`color(blue)"take the square root of both sides"`

`sqrt((y-8)^2)=+-sqrt49larrcolor(red)" note plus or minus"`

`rArry-8=+-7`

`"add 8 to both sides"`

`ycancel(-8)cancel(+8)=8+-7`

`rArry=8+-7`

`y=8+7rArry=15larr" is a solution"`

`y=8-7rArry=1larr" is a solution"`

`color(blue)"As a check"`

`y=15to(15-8)^2=7^2=49larr" true"`

`y=1to(1-8)^2=(-7)^2=49larr" true"`

Answer 2

15 or 1

Explanation:

Each side is a perfect square, so we just need to square root each side, so `(y-8)^2=49` becomes `y-8="+/-"7`. All numbers need to be put onto one side so `y-8="+/-"7` becomes `y=8"+/-"7`.

`y=8+7=15`
or
`y=-7+8=1`.