Surds (AS Maths Core1)

Surds

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Simplify Surds

Simplify the surd down to the biggest square number divisible in it.

For example:

1. 4√3 + √12 ---------> (√12 = √4x3 = √4x√3 = 2√3 ---- the 4 is square rooted to 2 and placed  outside the bracket)

-----------> 4√3 + 2√3 = 6√3

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2. (√48 + 2√27)/√12 ---------> (√48 = 4√3) (2√27 = 6√3) -----> 4√3+6√3 = 10√3 (10√3 = √300)

-----> √300 / √12 = √25 = 5

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Rationalise Surds

Rationalising the denominator so that an expression will get rid of the surds at the bottom of the fraction.

For example (write them out in column format on paper):

1. 5/√2 --------> 5/√2 x √2/√2 = (5x√2)/(√2x√2) = 5√2/2

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2. 7/(5√2-1) ------> (x both top and bottom by 5√2+1 so that it cancels out)

------> 7(5√2+1)/(5√2-1)(5√2+1) = 7+35√2/9 (the bottom fraction should cancel out to 9)

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