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Manipulating radicals

Manipulating radicals. Manipulating radicals. and. Also:. You should also remember that, by definition, √ a means the positive square root of a. When working with radicals it is important to remember the following two rules:. Simplifying radicals.

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Manipulating radicals

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  1. Manipulating radicals

  2. Manipulating radicals and Also: You should also remember that, by definition, √a means the positive square root of a. When working with radicals it is important to remember the following two rules:

  3. Simplifying radicals We can do this using the fact that For example: Simplify by writing it in the form We are often required to simplify radicals by writing them in the form Start by finding the largest square number that divides into 50. This is 25. We can use this to write:

  4. Simplifying radicals Simplify the following radicals by writing them in the forma√b.

  5. Adding and subtracting radicals Start by writing and in their simplest forms. Radicals can be added or subtracted if the number under the square root sign is the same. For example:

  6. Multiplying binomials containing radicals Simplify the following: Problem 2) demonstrates the fact that (a – b)(a + b) = a2 – b2. In general:

  7. Rationalizing the denominator Simplify the fraction . In this example we rationalize the denominator by multiplying the numerator and the denominator by × 5 5 = × When a fraction contains a radical as the denominator we usually rewrite it so that the denominator is a rational number. This is called rationalizing the denominator. For example: 2

  8. Rationalizing the denominator 2 3 1) 2) 3) 4 × × × 2 2 3 3 = = = 4 × × × Simplify the following fractions by rationalizing their denominators. 3 5 28

  9. Rationalizing the denominator Simplify When the denominator involves sums of differences between radicals we can use the fact that (a – b)(a + b) = a2 – b2 to rationalize the denominator. For example:

  10. Rationalizing the denominator Working: More difficult examples may include radicals in both the numerator and the denominator. For example: Simplify = 6 + 1

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