Question

How do you solve `(18-n)^(1/2)=(n/8)^(1/2)`?

Answer 1

`n = 16`

Explanation:

This is much easier to solve than it first appears. Notice that both powers are the same on each side of the equality. If the powers are the same and they are equal, the the bases must also be equal. Therefore:

`(18 - n ) = (n/8)`

So solve for `n`:

`18 - n = n/8 => 144 -8n = n => 144 = 9n => n = 144/9=> n=16`

Check:

`(18-16)^(1/2) = (16/8)^(1/2)`

`2^(1/2)= 2^(1/2)`