SURDS
CSEC ADD MATHS
EXAMPLES OF SURDS
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We know that a perfect square has an exact square root.
Examples: √16 = 4; √625 = 25
However, most numbers do not have exact square roots, that is
their square roots are not whole numbers. We cannot obtain
their exact result in a decimal form.
The square roots of these numbers are what we call surds.
EXAMPLES OF SURDS
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DEFINITION OF SURDS
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RULES FOR OPERATIONS ON SURDS
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Rules for surds are the same as the rules for simplifying roots
and involve the same rules for basic algebra.
Applying this rule, we have
√5 × √15 = √5 × (√3√5) = 5√3
RULES FOR OPERATIONS ON SURDS
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2.
a)
b)
c)
RULES FOR OPERATIONS ON SURDS
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RULES FOR OPERATIONS ON SURDS
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RULES FOR OPERATIONS ON SURDS
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RATIONALISING A SURD
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To rationalise a surd, we remove all surds from the denominator
of the expression, without changing its numerical value.
In this way, surds may now appear in the numerator of the
expression, where there may not have even had any from before.
1.
RATIONALISING A SURD
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RATIONALISING A SURD
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2.
RATIONALISING A SURD
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3.