Example 1
In this example, we split the square root
into two other square roots (9 and 5). We
can reduce sqrt 9 to 3 and are so able to
give a simplified answer.

Example 2
In this example, we multiplied two sqrts
together which gave us the sqrt of 144
that we can reduce to 12.

Example 3
In this example, we divided the two sqrts
by each other to give us the sqrt of 4.

Example 1
In this example, we have a similar
situation to the one in the example above.
We apply the same method to rationalise
the denominator.

Example 2
In this example, we have a number as the numerator and a number
and a surd as a denominator. To rationalise the denominator, we just
times the fraction by sqrt 2 / sqrt 2 (=1) which gives us 2 times 2
which is equal to 4 as the new denominator and then we just need to
solve the top by multiplying 5 and sqrt 2 which is 5 sqrt 2.

Example 3
In this last example, we have a number multiplied by a surd on the top and bottom of the fraction. The procedure is still,
the same, we times the fraction by sqrt 6 / sqrt 6 which gives us 7 sqrt 48 as the numerator and 30 as the denominator
of the rationalised fraction.

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Chapter 7.3: Learning Outcomes
Students will know what surds are!
Students will be able to simplify surds!
Students will be able to rationalise denominators in surd form!

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