# How To Solve Square Root Problems

This is the special symbol that means "square root", it is like a tick, and actually started hundreds of years ago as a dot with a flick upwards.It is called the radical, and always makes mathematics look important! We can use Imaginary Numbers, but that leads to a wrong answer of −4 Oh that's right ...For example, if you are given the square root √4, you can think of it as “the number that, when squared, equal four.” The correct answer would be 2, because when 2 is squared, it equals 2 X 2 = 4.But what if the number under the square root sign isn’t a perfect square? So if you are given the problem √12, you would factor it to get √(2 X 2 X 3), or √(4 X 3).

For example, to solve the problem 2√2 X 3√8, you would multiply the 2 and 3 together first, to get 6, and then you would multiply together the numbers inside of the square root and simplify your answer.The rule only works when x and y are both greater than or equal to 0 So we can't use that rule here.The first step to solving square roots is knowing how to simplify them.Then they would almost certainly want us to give the "exact" value, so we'd write our answer as being simply " To simplify a term containing a square root, we "take out" anything that is a "perfect square"; that is, we factor inside the radical symbol and then we take out in front of that symbol anything that has two copies of the same factor. On a side note, let me emphasize that "evaluating" an expression (to find its one value) and "solving" an equation (to find its one or more, or no, solutions) are two very different things.In the first case, we're simplifying to find the one defined value for an expression.So the problem would look like this: 2√2 X 3√8 = (2X3)√(2X8) = 6√16 = 6X4 = 24 Dividing by square roots gets a bit more complicated.Sometimes, you can just cancel out the denominator or simplify it.The cube root of 8, then, is 2, because 2 × 2 × 2 = 8.Notice that the symbol for cube root is the radical sign with a small three (called the ) above and to the left .For example, if you were given the problem √8/√2, you could divide the numerator and the denominator by √2, which would leave you with √4/1, or 2.So the problem would look like this: √8/√2 = √(8/2)/√(2/2) = √4/1 = √4 = 2 You could also come across a more complicated difference, such as √2/√3. Remember one simple rule: the denominator can never be a radical (a square root).

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