SOLUTION: I still don't get this square root thing - can someone please explain? Solve using the square root property: (x+8)^2 = 81

Question 114337: I still don't get this square root thing - can someone please explain?
Solve using the square root property:
(x+8)^2 = 81
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
A square root of a number is another number, when multiplied by itself results in the original number. 2 is a square root of 4, for example. The thing is, whenever you take a square root, you need to consider both the positive and the negative, because -2 is also a square root of 4.

So let's look at your problem:

The first thing you need to do is take the square root of both sides of the equation. Beginning with the left side of the equation, remember that for any real number a. On the right side of the equation, ask yourself, what number when multiplied by itself equals 81? I sincerely hope you came up with both 9 and -9.

So now we can re-write the equation like this:

or

or

or

Let's check to see if the answers make the original statement true:

=> , so that answer checks
=> so that answer checks as well.

If you are confused at all about the fact that there are two answers, don't worry. Having two answers for a 2nd-degree equation (one that has an or term in it) is part of the great and wonderful pattern of mathematics. You'll discover later on that 3rd-degree equations, such as things with an in them will have THREE solutions or roots. In fact, the fundamental theorem of algebra tells us that an n-th degree equation has n roots. For the time being, have faith. It will all make good sense in the end.

Hope that helps,
John
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