# Radicals - If n is even If n is even then a and b must be...

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If n is even: If n is even, then a and b must be nonnegative for the root to be a real number. If n is even and a is negative, then the root is not a real number. If n is odd: If n is odd, then a and b can be any real number.

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Things to note about radicals in general: for the nth radical or nth root, you want the expression that, when you raise it to the nth power, you would get the radic When there is no index number, n , it is understood to be a 2 or square root. For example: = principal square root of x . Note that NOT EVERY RADICAL is a square root. If there is an index number n other than the number 2, then you have a root other than a square root. Example 1 : Evaluate or indicate that the root is not a real number. View a video of this example The thought behind this is that we are looking for the square root of 100. This means that we are looking for a number that when we square it, we get 100. What do you think it is? Let’s find out if you are right: Since 10 squared is 100, 10 is the square root of 100.

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View a video of this example Now we are looking for the square root of -100, which means we are looking for a number that when we square it we get -100. What do you think it is? Let’s find out if you are right: Since there is no such real number that when we square it we get -100, the answer is not a real number. rule If n is an even positive integer, then If n is an odd positive integer, then If a problem does not indicate that a variable is positive, then you need to assume that we are dealing with both positive and negative real numbers and use this rule. Example 4 : Simplify .
View a video of this example Since it didn’t say that y is positive, we have to assume that it can be either positive or negative. And since the root number and exponent are equal, then we can use the rule. Since the root number and the exponent inside are equal and are the even number 2, we need to

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## This note was uploaded on 02/18/2011 for the course MATH 101 taught by Professor Kindle during the Spring '11 term at South Texas College.

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Radicals - If n is even If n is even then a and b must be...

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