 # Surds

## What are surds?     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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WHERE MATHS IS AT YOUR FINGERTIPS!  ULTIMATE MATHS Becoming an Accomplished Mathematician Ultimate Maths is a professional maths website that gives students the opportunity to learn, revise and apply different maths skills. We provide a wide range of lessons and resources...  Quality Content A wide range of quality learning resources is at your disposal. Effective Teaching Explanations, examples and questions combined for an effective learning experience. Easy Navigation A simple user interface ensures that you find the topics you are looking for.       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!      ## NOT CURRENTLY AVAILABLE! 