Question

How do you solve `sqrtn-3=6` and check your solution?

Answer 1

See the entire solution and verification process below:

Explanation:

Step 1) Add `color(red)(3)` to each side of the equation to isolate the `n` term while keeping the equation balanced:

`sqrt(n) - 3 + color(red)(3) = 6 + color(red)(3)`

`sqrt(n) - 0 = 9`

`sqrt(n) = 9`

Step 2) Square each side of the equation to solve for `n` while keeping the equation balanced:

`(sqrt(n))^2 = 9^2`

`n = 81`

To check the solution we substitute `color(red)(81)` for `color(red)(n)`, evaluate the left side of the equation and ensure it equals the right side of the equation:

`sqrt(color(red)(n)) - 3 = 6` becomes:

`sqrt(color(red)(81)) - 3 = 6`

`9 - 3 = 6`

`6 = 6`