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Published byFrank Clarke Modified over 4 years ago

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Checking Factoring The checking of factoring can be done with the calculator. Graph the following expressions: 1.x 2 + 5x – 6 2.(x – 3)(x – 2) 3.(x + 6)(x – 1) What do you notice? Are they the same graph? Discuss what you can conclude from the graphs.

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Roots What is the value of 2 2 ? What is x? However: x = In this case 2 is considered the principal root or the nonnegative root, when there is more than one real root. Finding the square root of a number and squaring a number are inverse operations. WHY? Should be 2, right?

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Roots What is the value of The values found are known as the nth roots and are also principal roots. The following is the format for a radical expression. index radical sign radicand

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Roots of Summary of the real nth roots. Real nth Roots of b,, or – nb > 0b < 0b = 0 even one positive root one negative root no real roots one real root, 0 odd one positive root no negative roots no positive roots one negative root

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Practice with Roots Simplify the following. 1. 2. 3. 4. 5. has to be absolute value to identify principal root Estimated between 5 and 6 because 5 2 = 25 and 6 2 = 36.

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Radical Expressions Radical “like expressions” have the same index and same radicand. Product and Quotient Properties:

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Simplifying Radical Expressions 1.The index, n, has to be as small as possible 2.radicand NO factors, nth roots 3.radicand NO fractions 4.NO radical expressions in denominator For example:

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More examples: Simplifying Radical Expressions

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More examples: Simplifying Radical Expressions

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Radical Expressions Conjugates ± same terms Multiply the following:

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Radical Expressions Deduction about conjugates: Product of conjugates is always a rational number. For example:

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Radical Expressions Simplify the following

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Radical Expressions In-Class work Rationalize the denominator:

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