Surds (AS Maths Core1)

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

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)