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Indices and Surds

Indices and Surds. Here b is called the Index. This means a to the power of b . . This gives us our first rule of indices. This gives us our second rule of indices. Page 112 Exercise 1 Page 113 Exercise 2. This gives us our third rule of indices. Page 113 Exercise 3. Harder Examples.

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Indices and Surds

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  1. Indices and Surds

  2. Here b is called the Index This means a to the power of b. This gives us our first rule of indices This gives us our second rule of indices

  3. Page 112 Exercise 1 Page 113 Exercise 2

  4. This gives us our third rule of indices Page 113 Exercise 3

  5. Harder Examples Page 114 Exercise 4B

  6. Zero and negative indices Rule 4 Rule 5

  7. Page 115 Exercise 5A and 5B

  8. Fractional Indices This gives us rule 6:

  9. = 4 Revision: Page 116 117 Exercise 6A and 6B

  10. Surds () Irrational Numbers: Numbers that can not be written as a fraction. A surd is a special irrational number. It is a square root, cube root, etc. that can not be expressed as a rational number.

  11. When simplifying a surd always look for a square number as a factor.

  12. Page 121 Exercise 8A Page 122 Exercise 8B Up to and including Question 7 Page 123 Check up Exercise

  13. Rationalising a Surd Denominator A surd is an irrational number If we have a surd as a denominator we should attempt to rationalise the denominator by removing the surd. i.e. make the denominator into a rational number. What is the only number we can multiply by and not change the value of the number we start with? The answer of course is 1. Remember we can write the number one in many different ways.

  14. This is a fraction with a rational denominator.

  15. This is a fraction with a rational denominator.

  16. Things get a little more complicated when we get a fraction like Here we have to remember the properties of a difference of two squares. So we end up with a whole number.

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