Solution 1.3:5a

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Current revision (14:22, 22 September 2008) (edit) (undo)
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The number
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The number 4 can be written as <math>4=2\centerdot 2=2^{2}</math> and then, using the power rules, we obtain
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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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{{Displayed math||<math>4^{\frac{1}{2}} = \bigl(2^{2}\bigr)^{\frac{1}{2}} = 2^{2\cdot \frac{1}{2}} = 2^{1} =2\,</math>.}}
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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 <math>4^{\frac{1}{2}}</math> is <math>\sqrt{4}</math> (the square root of 4); more on this in the section on roots later in the course.
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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.
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Current revision

The number 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}} = \bigl(2^{2}\bigr)^{\frac{1}{2}} = 2^{2\cdot \frac{1}{2}} = 2^{1} =2\,.

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

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