Solution 1.3:5a

From Förberedande kurs i matematik 1

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The number
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<center> [[Image:1_3_5a.gif]] </center>
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<math>4</math>
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can be written as
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<math>4=2\centerdot 2=2^{2}</math>
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and then, using the power rules, we obtain
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<math>4^{\frac{1}{2}}=\left( 2^{2} \right)^{\frac{1}{2}}=2^{2\centerdot \frac{1}{2}}=2^{1}=2</math>
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NOTE: another way to denote
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<math>4^{\frac{1}{2}}</math>
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is
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<math>\sqrt{4}</math>
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(the root of
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<math>4</math>
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); more on this in the section on roots later in the course.

Revision as of 12:00, 15 September 2008

The number \displaystyle 4 can be written as \displaystyle 4=2\centerdot 2=2^{2} and then, using the power rules, we obtain


\displaystyle 4^{\frac{1}{2}}=\left( 2^{2} \right)^{\frac{1}{2}}=2^{2\centerdot \frac{1}{2}}=2^{1}=2

NOTE: another way to denote \displaystyle 4^{\frac{1}{2}} is \displaystyle \sqrt{4} (the root of \displaystyle 4 ); more on this in the section on roots later in the course.

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