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April 13th, 2011, 12:09 PM  #1 
Newbie Joined: Apr 2011 Posts: 3 Thanks: 0  Help with radicals
I found this problem in a math book: ?(y) + 2 = ?(y + 16) The answer in the back says that y = 9, and it works when you substitute it back in the equation, but I can't figure out how to solve it. 
April 13th, 2011, 12:32 PM  #2 
Global Moderator Joined: Oct 2008 From: London, Ontario, Canada  The Forest City Posts: 7,814 Thanks: 1046 Math Focus: Elementary mathematics and beyond  Re: Help with radicals
Square both sides and you'll be left with a single radical. Isolate the radical on one side of the equation and square both sides again, then solve for y.

April 13th, 2011, 01:03 PM  #3 
Newbie Joined: Apr 2011 Posts: 3 Thanks: 0  Re: Help with radicals
When I square both sides, don't I get y + 4 = y +16 ? 
April 13th, 2011, 01:10 PM  #4 
Senior Member Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,170 Thanks: 472 Math Focus: Calculus/ODEs  Re: Help with radicals
No, let's start with the original: Square both sides: Subtract y + 4 from both sides: Divide through by 4: Square both sides: 
April 13th, 2011, 01:14 PM  #5 
Newbie Joined: Apr 2011 Posts: 3 Thanks: 0  Re: Help with radicals
Got it! No wonder I couldn't make it work. Thanks so much. 
April 13th, 2011, 01:19 PM  #6 
Senior Member Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,170 Thanks: 472 Math Focus: Calculus/ODEs  Re: Help with radicals
You're welcome, and welcome to the forum! 
April 13th, 2011, 03:40 PM  #7 
Senior Member Joined: Apr 2007 Posts: 2,140 Thanks: 0 
?y + 2 = ?(y + 16) (?y + 2)² = ?(y + 16)² y + 4?y + 4 = y + 16 4?y = 16  4 = 12 ?y = 12/4 = 3 ?y² = 3² ? y = 9 

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