Question

How do you solve `(p + 7) ^ { 2} = 216`?

Answer 1

`p=-7+-6sqrt6`

Explanation:

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

`sqrt((p+7)^2)=+-sqrt216larrcolor(blue)"note plus or minus"`

`rArrp+7=+-6sqrt6`

`"subtract 7 from both sides"`

`pcancel(+7)cancel(-7)=-7+-6sqrt6`

`rArrp=-7+-6sqrt6larrcolor(red)"exact solutions"`

Answer 2

`p=-7+-6sqrt(6)`

Explanation:

`(p+7)^2=216`

`rarr p+7 = +-sqrt(216)`

`color(white)("XXX")226 =2^2 * 3^2 * 6 =6^2 * 6`

`rarr p+7 =+-6sqrt(6)`

`rarr p=-7+-sqrt(6)`

Answer 3

`p ~~ 7.70`

Explanation:

Alright, so we need to isolate the `p` on one side of the equation so that we can solve this.

To do that, we are going to start with taking the square root of both sides.

`sqrt((p+7)^2) = +-sqrt(216)`

The square root and the square will cancel out so all we have to do is finish the equation!

`p+7~~14.70`
`p +7-7~~ 14.70-7`
`p ~~ 7.70`

Also, I would like to add that is not the exact number, IT IS AN APPROXIMATION. If you would like to have the exact number, see below. Since `sqrt(216)` can not be completely squared, it would have to be reduced to

`p+7=+-sqrt(216)`
`p+7=+-6sqrt(6)`
`p=-7+-6sqrt(6)`

Hope that helps!
~Chandler Dowd