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# solve using the square root property

x^2+216=0 I am having problems finishing this equation, I end up with x= + or - the square root of 216. Can anybody help?

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Matt L. | MIT/Harvard Grad for Academic Tutoring & Test PrepMIT/Harvard Grad for Academic Tutoring &...
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### Comments

Yes this helps. Thank you very much.

Timothy B. | Math (Algebra, Calculus), Physics, Chemistry - 6th-12th gradeMath (Algebra, Calculus), Physics, Chemi...
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Well Greg, thanks for asking.

x^2 + 216 = 0

Step by step solving we get:
x^2 + 216 = 0
squareroot(x^2 + 216) = squareroot (0)
sqrt(x^2) + sqrt(216) = 0
x + sqrt(216) = 0
x = -sqrt(216)

I hope this helps :)

### Comments

Timothy, this isn't correct. In your second line, you took the square root of both sides of the equation, which is fine, but then in your third line you made the classic mistake of assuming squareroot(a+b)=squareroot(a)+squareroot(b) But this is definitely false! You can't break up square roots over sums or differences. To see why, just look at a simple example; choose a=8 and b=8. squareroot(8+8)=squareroot(16)=4 but squareroot(8)+squareroot(8) =2squareroot(8) definitely isn't 4! (In fact, it's greater than 4.) So be careful! You can only break up square roots over products and quotients, not over sums and differences. To solve the given equation, you first must pull 216 to the other side, and THEN take square roots.

Thanks for correcting me. I appreciate it. I was doubtful in the first place but it's good that I know now. You're right though. I was reading your answer because I thought the same thing, the problem must have been written incorrectly.