3.2 multiplying & dividing radicals
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3.2 Multiplying and Dividing Radicals
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3.2 Multiplying and Dividing Radical Expressions
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Multiplying Radical ExpressionsGeneral Rule
In your own words, what does this mean?
where k is a natural number, and m, n, a, and b are real numbers.
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Eg. Multiply, simplify the products where possible.
IF NEEDED
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RECAPThere was a lot of panic...
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RECAPRestrictions
Only needed when there is/are unknown(s) in the radicand.
Technically only needed when the index is EVEN
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RECAPWhy does work while does not?
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RECAPWhy does work as well as ?
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Shockingly simple examples that mess people up...
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Shockingly simple examples that mess people up...
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Eg. Multiply, simplify the products where possible.
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Eg. Multiply, simplify the products where possible.
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Dividing Radical ExpressionsGeneral Rule
In your own words, what does this mean?
where k is a natural number, and m, n, a, and b are real numbers and n ≠ 0 and b ≠ 0.
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Eg.15√453√5
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ReviewIs this radical in simplest form?
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To get rid of the radical on the bottom, we have to rationalize the denominator.
If there is only a single radical, we just multiply the numerator and denominator by the same radical.
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E.g.
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E.g.
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If a denominator is a binomial that contains a square root, multiply the numerator and the denominator by a conjugate of the denominator.
The conjugate is the same binomial, just a different operator in the middle:
If the original binomial is (x + y), the conjugate is____________________
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The product of a pair of conjugates is a difference of squares.
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Therefore...
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E.g.
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E.g.
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E.g.
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page 289#1(ad), 2(ad), 3(acd), 4(abce), 5(ac), 6(ad), 9(a), 10
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