Solving Square Root Problems

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The negative sign outside of the radical means that our answer will be negative, but we don't really have to worry about that until the end. In particular, we want one of those factors to be a perfect square.

Unfortunately, 8 nor 3 are perfect squares, so we need to see if there is another way to simplify.

For example, is not a problem since (-2) • (-2) • (-2) = -8, making the answer -2.

In cube root problems, it is possible to multiply a negative value times itself three times and get a negative answer.

There simply is no way to multiply a number times itself and get a negative result. As research with imaginary numbers continued, it was discovered that they actually filled a gap in mathematics and served a useful purpose.

Imaginary numbers are essential to the study of sciences such as electricity, quantum mechanics, vibration analysis, and cartography.We first have to think of "what number squared is 4? Let's write it like this: Since 18 is not a perfect square, we must simplify this expression by rewriting it as a product of 2 square roots.We want to rewrite this so that one of the factors is a perfect square. Did you notice how we rewrote the square root of 18 as the product of 2 factors, and one of them was a perfect square?As soon as you see that you have a pair of factors or a perfect square, and that whatever remains will have nothing that can be pulled out of the radical, you've gone far enough.An equation that contains a radical expression is called a radical equation.In the first case, we're simplifying to find the one defined value for an expression.In the second case, we're looking for any and all values what will make the original equation true.That is, we find anything of which we've got a pair inside the radical, and we move one copy of it out front.When doing this, it can be helpful to use the fact that we can switch between the multiplication of roots and the root of a multiplication.This tucked-in number corresponds to the root that you're taking.For instance, relating cubing and cube-rooting, we have: ".

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