Expert I Number Sense (11)

Question 1

How do you add radicals?

Answer 1

You can only add radicals when the radicand and the index are the exact same. Basically the radical portion behaves like a variable, where it must be the same in order for it to be added just like adding like terms.

In the example the index of all of these is two so we didn’t need to worry about that as much, but sometimes the index could also be another number, and in that case you are not permitted to add the radicals.

You may need to manipulate the radicals so that they are in lowest terms in order to have the radicands match. Make sure that you know how to convert from an entire radical to a mixed radical in order to do this. Most students convert using knowledge of factors. See the grade 10 material to help with factoring and roots as well as a card on converting from entire to mixed radical.

Question 2

absolute value

Answer 2

If x is positive, then the absolute value of negative x is positive x. The absolute value of positive x is positive x.

|-x| = x

|x| = x

Thus the result is always positive no matter what.

Question 3

How do you multiply radicals?

Answer 3

If the index is the exact same, you can multiply the stuff under the radical sign together with just one single radical sign around the multiplication.

Question 4

How do you rationalize the denominator?

Answer 4

If there is a radical sign in the denominator, you must multiply the top and bottom of the fraction by that same thing. The amount of times you multiply depends on the index. If you have a square root in the denominator you will just square the denominator in order to no longer have an irrational number in the denominator. If you have a cubed root in the denominator, you will cube the denominator. If you have a two-term denominator, then you will need to multiply by something similar but switch the sign in between.

Question 5

How can you use factoring to simplify a rational expression?

Answer 5

If you can factor the same thing out of the numerator and the denominator of a fraction, then you are able to simplify the rational expression. Sometimes this can even make the denominator 1 and thus you will not have to deal with a fraction anymore so this is useful to do. The resulting equation will be easier to understand and to graph once you do this. The graphing portion of this is taught in math 30-1, but in math 20-1 you are expected to be able to factor and cancel out the common factors in the numerator and denominators.

Remember that you will need to know how to factor trinomials in order to do this! Factoring by decomposition is covered in the math 10 flashcards so feel free to check out those cards to get a solid review.

You can alternatively divide the numerator by the denominator using polynomial long division or synthetic division. These concepts are taught in math 30-1 and are used in math 31.

In grade 12 you will need to do this in order to graph rational equations so it is important to learn. In grade 12 you will need to be careful to not simplify until you have figured out your non-permissible values created by finding values that would cause a division by 0.