28 MULTIPLYING AND DIVIDING HERE IS THE RULE for multiplying radicals: It is the symmetrical version of the rule for simplifying radicals. Problem 1. Multiply. To see the answer, pass your mouse over the colored area.
Example 1. Multiply ( Solution. The student should recognize the form those factors will produce:
Problem 2. Multiply. a) ( b) (2 c) (1 + d) (
Problem 3. (x − 1 − a) What form does that produce?
The difference of two squares. x − 1 is "a." b) Multiply out.
Problem 4. Multiply out.
Dividing radicals For example,
Problem 5. Simplify the following.
Conjugate pairs The conjugate of a +
Example 2. Multiply 6 − Solution. The product of a conjugate pair -- (6 − -- is the difference of two squares. Therefore, (6 − When we multiply a conjugate pair, the radical vanishes and we obtain a rational number. Problem 6. Multiply each number with its conjugate. a) x + b) 2 −
d) 4 − Example 3. Rationalize the denominator:
Solution. Multiply both the denominator and the numerator by the conjugate of the denominator; that is, multiply them by 3 −
The numerator becomes 3 −
Problem 7. Write out the steps that show the following.
Problem 9. Here is a problem that Calculus students have to do. Write out the steps that show:
In this case, you will have to rationalize the numerator.
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