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Unformatted text preview: 4 z 24 (f) 3 9 x2 3 6 x2 [Solution]
(a) y 7
In this case the exponent (7) is larger than the index (2) and so the first rule for simplification is
violated. To fix this we will use the first and second properties of radicals above. So, let’s note
that we can write the radicand as follows. y7 = y6 y = ( y3 ) y
2 So, we’ve got the radicand written as a perfect square times a term whose exponent is smaller
than the index. The radical then becomes, y7 = (y ) 32 y Now use the second property of radicals to break up the radical and then use the first property of
radicals on the first term. y7 = (y ) 32 y = y3 y This now satisfies the rules for simplification and so we are done.
Before moving on let’s briefly discuss how we figured out how to break up the exponent as we
did. To do this we noted that the index was 2. We then determined the largest multiple of 2 that
is less than 7, the exponent on the radicand. This is 6. Next, we noticed that 7=6+1.
Finally, remembering several rules of exponents we can rewrite the radicand as, y 7 = y 6 y = y ( 3)( 2) y = ( y 3 ) y
2 In the remaining examples we will typically jump s...
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This note was uploaded on 06/06/2012 for the course ICT 4 taught by Professor Mrvinh during the Spring '12 term at Hanoi University of Technology.
- Spring '12