Solution 3.1:2b

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m (Lösning 3.1:2b moved to Solution 3.1:2b: Robot: moved page)
Current revision (07:52, 30 September 2008) (edit) (undo)
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That which is under the root sign is the same as <math>(-3)^{2} = 9</math> and because
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<center> [[Image:3_1_2b.gif]] </center>
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<math>9 = 3\cdot 3 = 3^{2}</math>, hence
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{{Displayed math||<math>\sqrt{(-3)^{2}} = \sqrt{9} = 9^{1/2} = \bigl(3^{2}\bigr)^{1/2} = 3^{2\cdot\frac{1}{2}} = 3^{1} = 3</math>.}}
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Note:
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The calculation <math>\sqrt{(-3)^{2}} = \bigl((-3)^{2}\bigr)^{1/2} = (-3)^{2\cdot \frac{1}{2}} = (-3)^1 = -3</math> is wrong at the second equals sign. Remember that the power rules apply when the base is positive.

Current revision

That which is under the root sign is the same as \displaystyle (-3)^{2} = 9 and because \displaystyle 9 = 3\cdot 3 = 3^{2}, hence

\displaystyle \sqrt{(-3)^{2}} = \sqrt{9} = 9^{1/2} = \bigl(3^{2}\bigr)^{1/2} = 3^{2\cdot\frac{1}{2}} = 3^{1} = 3.


Note: The calculation \displaystyle \sqrt{(-3)^{2}} = \bigl((-3)^{2}\bigr)^{1/2} = (-3)^{2\cdot \frac{1}{2}} = (-3)^1 = -3 is wrong at the second equals sign. Remember that the power rules apply when the base is positive.

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