Simplifying Radicals

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Simplifying Radicals
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Radicals
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Simplifying Radicals
Express 45 as a product using a square number
Separate the product
Take the square root of the perfect square
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Some Common Examples
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Harder Example
Find a perfect square number that divides evenly
into 245 by testing 4, 9, 16, 25, 49 (this
works)
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Addition and Subtraction
You can only add or subtract like radicals
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More Adding and Subtracting
You must simplify all radicals before you can add
or subtract
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Multiplication
Consider each radical as having two parts. The
whole number out the front and the number under
the radical sign.
You multiply the outside numbers together and you
multiply the numbers under the radical signs
together
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More Examples
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Try These
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Division
As with multiplication, we consider the two parts
of the surd separately.
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Division
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Important Points to Note
Radicals can be separated when you have
multiplication and division
However
Radicals cannot be separated when you have
addition and subtraction
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Rational Denominators
Radicals are irrational. A fraction with a
radical in the denominator should to be changed
so that the denominator is rational.
Here we are multiplying by 1
The denominator is now rational
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More Rationalising Denominators
Simplify
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Review Difference of Squares
When a radical is squared, it is no longer a
radical. It becomes rational. We use this and
the process above to rationalise the denominators
in the following examples.
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More Examples
Simplify
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Another Example
Simplify
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Try this one
Simplify
See next slide
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Continuing
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