square root problem

TeacherJamie

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Joined
Feb 11, 2008
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I am an elementary teacher who has been thrown into a situation above my easy capabilities. I need to help a middle school student understand his math, and I simply can't remember how to tackle this type of problem. The problem is this: the square root of d+9 (all of that is under the same root sign) plus three is equal to d. The student is having trouble because he points out you cannot separate the two addends which are under the root sign together. Any help is GREATLY appreciated. Thanks!!
 
Let me try and help you recollect.

\(\displaystyle \sqrt{d+9}+3=d\)

Subtract 3 from both sides:

\(\displaystyle \sqrt{d+9}=d-3\)

Now, square both sides:

\(\displaystyle d+9=(d-3)^{2}\)

\(\displaystyle d+9=d^{2}-6d+9\)

\(\displaystyle d^{2}-7d=0\)

\(\displaystyle d(d-7)=0\)

And we can see that d=0 and d=7 are solutions. But, one may be extraneous. Sub back into the original for a check to see.

Does that help?.
 
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