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

Info iconThis preview shows pages 1–6. Sign up to view the full content.

View Full Document Right Arrow Icon
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.
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
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.
Background image of page 2
Note that we are only interested in the principal root and since 100 is positive and there is not a sign in front of the radical, our answer is positive 10. If there had been a negative in front of the radical our answer would have been -10. Example 2 : Evaluate or indicate that the root is not a real number. View a video of this example Now we are looking for the negative of the fourth root of 16, which means we are looking for a number that when we raise it to the fourth power we get 16 (then we will take its negative). What do you think it is? Let’s find out if you are right: Since 2 raised to the fourth power is 16 and we are negating that, our answer is going to be -2. Note that the negative was on the outside of our even radical. If the negative had been on the inside of an even radical, then the answer would be no real number. Example 3 : Evaluate or indicate that the root is not a real number.
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
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 .
Background image of page 4
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
Background image of page 5

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Image of page 6
This is the end of the preview. Sign up to access the rest of the document.

Page1 / 23

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

This preview shows document pages 1 - 6. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online