Saw this at the bottom of a page about Chris Cornell and decided to solve it.  However, my solution didn't check out going the other way and, since it's been many years I'm wondering where I went wrong.
 
1)  To get rid of the square root symbols I squared both sides so now the equation reads (x + 15) + x = 225
2)  Subtract 15 from both sides to get x + x = 210, or 2x = 210
3)  Divide both sides by 2 to get x = 105
 
However, checking the answer shows that x has to be smaller than 105.
 
1)  The square root of 120 (105 + 15) is 10.95+
2)  The square root of 105 is 10.25+
3)  Obviously 10.95 + 10.25 is greater than 15...
 
Working it the other way by plugging in a few examples got me the real answer fairly quick (x = 49), but I'm trying to figure out where I did the normal solving wrong.
 
Solution:  
 
1)  The square root of (49 + 15) + the square root of 49 = 15
2)  The square root of 64 + the square root of 49 = 15
3)  8 + 7 = 15

The bat cost $0.95.

Try this:
 
Get the x+15 that is under the sq.rt. by itself and then square both side (i.e., subtract the sq.rt. of x from 15)
 
sq.rt.(x+15) = 15-sq.rt.(x)
 
square both side:
 
x+15 = (15-sq.rt.(x))^2
 
then deal with the (15-sq.rt.(x))^2
(15-sq.rt.(x))(15-sq.rt.(x))
225-15sq.rt.(x)-15sq.rt.(x)+x
225-30sq.rt.(x)+x
 
x+15 = 225-30sq.rt.(x)+x
0 = 210 - 30sq.rt.(x)
210 = 30sq.rt.(x)
7 = sq.rt.(x)
49 = x
 
 

craigb

 
Saw this at the bottom of a page about Chris Cornell and decided to solve it.  However, my solution didn't check out going the other way and, since it's been many years I'm wondering where I went wrong.
 
1)  To get rid of the square root symbols I squared both sides so now the equation reads (x + 15) + x = 225

(x + 15) + x is wrong.

There's two mush X in the ecwayshun.

49. I did it the dummies way...
 
Figured it should be a whole number for the square root value. Started with x = 25. Square root of 25 = 5. Plus square root of (25 +15) (i.e., 40) is ....no dice.
 
Okay. try next number 36. Square root of 36 is 6. Square root of (36+15) (i.e., 51) is .... no dice.
 
Okay, try next number 49. Square root of 49 is 7. Square root of (49+15) (i.e., 64) is 8. Ah-ha! Getting somewhere. 7 + 8 = 15. X= 49.
 
Grade 'A' for the answer. Grade 'F' for the solution mechanics.