REDUCE+SQUARE+ROOTS


 * REDUCING SQAURE ROOTS**

To simplify a square root, you "take out" anything that is a "perfect square"; that is, you take out front anything that has two copies of the same factor:
 * // Simplifying Square-Root Terms //**



Note that the value of the simplified radical is //positive//. While either of +2 and –2 might have been squared to get 4, "the square root of four" is //defined// to be //only// the positive option, +2. When you [|solve the equation] // x // 2 = 4 , you are trying to find //all// possible values that might have been squared to get 4. But when you are just simplifying the expression ,the ONLY answer is " 2 "; this positive result is called the "principal" root. (Other roots, such as –2, can be defined using graduate-school topics like "complex analysis" and "branch functions", but you won't need that for years, if ever.) Sometimes the argument of a radical is not a perfect square, but it may "contain" a square amongst its factors. To simplify, you need to factor the argument and "take out" anything that is a square; you find anything you've got a pair of inside the radical, and you move it out front. To do this, you use the fact that you can switch between the multiplication of roots and the root of a multiplication. In other words, radicals can be manipulated similarly to powers:

There are various ways I can approach this simplification. One would be by factoring and then taking two different square roots: The square root of 144 is ** 12 **. You probably already knew that 122 = 144, so obviously the square root of 144 must be 12. But my steps above show how you can swich back and forth between the different formats (multiplication inside one radical, versus multiplication of two radicals) to help in the simplification process. Neither of 24 and 6 is a square, but what happens if I multiply them inside one radical? This answer is pronounced as "five, root three". It is proper form to put the radical at the end of the expression. Not only is " " non-standard, it is very hard to read, especially when hand-written. And write neatly, because " " is not the same as " ".
 * **Simplify [[image:rad009.gif]]**
 * **Simplify[[image:24_26.gif]]**
 * ** Simplify[[image:75.gif]] **

For Fun Games Based on Reducing Square Roots go to: [] Created by Dawit Samson**
 * Contributed by [|www.purplemath.com]