Surds Multiplication and Rationalisation Techniques
Learn about surds multiplication, rationalisation, and solving equations using index and surd rules. Practice various exercises to enhance your understanding.
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Presentation Transcript
? ? + ? ? Surds Multiplication And DOTs ? + ?
Surds Multiplication BAT simplify and rationalise surds BAT solve equations using the rules for indices and surds KUS objectives Starter: ?? ?? ? ? ? ?? ? ?? ? 5 ? ? ? ?
WB29a Explore making an integer Multiply each of the given numbers by a single term to give an integer answer 3 2 5 2 7 3 + 2
WB29b making an integer (2 + 3) (2 - 3) Multiply by the conjugate = 4 - 2 3 + 2 3 - 3 3 = 4 + 0 - 3 = 1 This is the same structure as difference of squares for quadratics (1 + 5)(1 - 5) Now try these: (6 + 2 3)(6 - 2 3)
Practice 1: Rationalise these! 3 1 + 3 1 + 2 3 7 4 + 7 5 + 3 7 5 1 5 2 5 + 2 2 3 3 + 4 3 3 - 6 5 6 2 - 7 2 7- 3 10 5 10 4 7 - 3 5
Summary Notes: Rationalise a surd This is a trick to make the denominator an integer when you have a surd as a denominator. First make sure you are happy that a a = a (a + b)(a - b) = a2 b2 and 11 11 = 11 (7 + 11) (7 - 11) = 49 11 11 = 49 11 = 38
KUS objectives BAT simplify and rationalise surds BAT solve equations using the rules for indices and surds self-assess One thing learned is One thing to improve is
