Expressions Containing Square Roots

Notes on expressions containing square roots

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Algebra: Techniques
Section 3: Expressions involving square roots
Notes and Examples
These expressions can be treated in a similar way to algebraic ones i.e. by
collecting like terms and / or multiplying out brackets. They can be simplified
by using knowledge of square numbers and rationalised so that the
denominator of a fraction is always an integer rather than a square root term.
Remember that a a a
Example 1
Simplify if possible:
(i) 128 (ii) 75 48 (iii) 12 3
(iv) 2 3 3 3
(v) 1 2 1 2
Solutions
(i) 128 64 2 8 2
(ii) 75 48 25 3 16 3 5 34 3 3
(iii) 12 3 2 3 3 6
(iv) 2 3 3 3 6 3 3 2 3 3 3 3
(v) 1 2 1 2 1 2 2 2 1
Note with this last example that the product gives an
answer that does not contain a square root. It is just the
difference of two squares again.
You can see further examples on manipulating surds using the Flash resource
Working with surds and Rationalising the denominator.
You can test yourself using the interactive questions Adding and subtracting
surds, Multiplying surds and Rationalising the denominator.
© MEI, 24/07/09 1/1