0.3_bzca5e

0.3_bzca5e - root of a natural number that is not a perfect...

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Section P3 Radicals and Rational Exponents

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Square Roots
81 9 40 9 7 9 3 64 8 = - + = - = 2 Definition of the Principal Square Root If a is a nonnegative real number, the nonnegative number b such that b =a, denoted by b= a is the principal square root of a.

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Examples 36 16 100 44 121 - + - Evaluate
Simplifying Expressions of the Form 2 a

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The Product Rule for Square Roots

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A square root is simplified when its radicand has no factors other than 1 that are perfect squares.
Examples 4900 Simplify:

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Examples 4 63 x x × Simplify:
The Quotient Rule for Square Roots

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Examples Simplify: 3 9 49 54 2 x x

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Two or more square roots can be combined using the distributive property provided that they have the same radicand. Such radicals are called like radicals .

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Example 10 5 2 5 3 6 3 12 - + - Add or Subtract as indicated:
Example 7 98 2 5 28 x x x x + - - Add or Subtract as indicated:

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Rationalizing Denominators
Rationalizing a denominator involves rewriting a radical expression as an equivalent expression in which the denominator no longer contains any radicals. If the denominator contains the square

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Unformatted text preview: root of a natural number that is not a perfect square, multiply the numerator and the denominator by the smallest number that produces the square root of a perfect square in the denominator. Let’s take a look two more examples: Examples 7 6 7 18 Rationalize the denominator: Examples 2 3 2 5 + Rationalize the denominator: Other Kinds of Roots Examples 3 3 4 8 8 16-Simplify: The Product and Quotient Rules for nth Roots Example 4 5 5 6 81 4 40 × Simplify: Example 3 3 3 64 27 250 2 16-Simplify: Rational Exponents Example 3 4 3 5 5 3 1 2 81 32 48 3 x x Simplify: Example 5 4 1 5 3 2 4 2 81 x x x ÷ ÷ Simplify: Notice that the index reduces on this last problem. (a) (b) (c) (d) 3 81 4 x x Simplify: 9 2 9 2 9 2 9 2 x x x x x x (a) (b) (c) (d) 2 3 1 4 2 7 3 x x ÷ ÷ Simplify: 5 4 5 4 7 4 7 4 21 63 21 63 x x x x...
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0.3_bzca5e - root of a natural number that is not a perfect...

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