Question

How do you solve `sqrt(2n-88)=sqrt(n/6)`?

Answer 1

The solution of the equation is `n = 48`.

Explanation:

First, you must get rid of the radicals. In this case, that is achieved by squaring both sides of the equation.

`(sqrt(2n - 88))^2 = (sqrt(n/6))^2`

`2n - 88 = n/6`

Now use inverse operations to solve for `n`.

`(2n - 88)6 = (n/6)6`

`12n - 528 = n`
`12n - 12n - 528 = n - 12n`
`-528 = -11n`
`(-528)/-11 = (-11n)/-11`

`48 = n`

Now we must check the solution to be sure that it is not extraneous. This step absolutely cannot be skipped when solving radical equations! Remember to check a solution, we put it in place of the variable in the original equation and simplify each side of the equation to see if it makes a true statement.

`sqrt(2*48 - 88) = sqrt(48/6)`

`sqrt(96 - 88) = sqrt(8)`
`sqrt(8) = 2sqrt(2)`
`2sqrt(2) = 2sqrt(2)`

Since the two sides of the equation simplify to be equal, `48` is the solution of the equation.