simplifying radicals radicals simplifying radicals express 45 as a product using a square number...
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Simplifying Radicals
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Radicals
2 5 10
623
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Simplifying Radicals
45 59
59
53
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
12 3434
32
75 325325
35
18 2929
23
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Harder Example
245 Find a perfect square number that divides evenly into 245 by testing 4, 9, 16, 25, 49 (this works)
549
549
57
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Addition and Subtraction
You can only add or subtract “like” radicals
535 54
773 72
236325 6322 You cannot add or subtract with
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More Adding and Subtracting
83775
2437325
You must simplify all radicals before you can add or subtract
223735
22312
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Multiplication
5327 1021
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
756 425
6238 1816 Note that can be simplified
18
2916
2316
248
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Try These
2463 1212 153107
15021
62521
6105
3412
324
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Division
531012 53
1012
As with multiplication, we consider the two parts of the surd separately.
5
104
24
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Division
35758 35
758
3
75
5
8
255
8
55
8
8
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Important Points to Note
baab
bab
a
However baba
baba
Radicals can be separated when you have multiplication and division
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.
5
3
5
5
5
3
Here we are multiplying by 1
5
53
The denominator is now rational
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More Rationalising Denominators
35
6
3
3
35
6
15
36 Simplify
Multiply by 1 in the form 3
3
5
32
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Review Difference of Squares
))(( baba 22 bababa 22 ba
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
35
6
35
35
35
6
925
)35(6
Simplify
16
)35(6
Here we multiply by 5 – which is called the conjugate of 5 + 3
3
8
)35(3
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Another Example
73
21
73
73
73
21
73
14763
Simplify
Here we multiply by the conjugate of which is
73 73
4
14763
4
14763
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Try this one
352
56
352
352
352
56
9254
3518510302
Simplify
320
3523510302
The conjugate of
is 352 352
17
3523510302 See next
slide
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Continuing
17
3523510302
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