Solution 3.1:2b

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m (Lösning 3.1:2b moved to Solution 3.1:2b: Robot: moved page)
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That which is under the root sign is the same as
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<center> [[Image:3_1_2b.gif]] </center>
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<math>\left( -\text{3} \right)^{\text{2}}=\text{9 }</math>
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and because
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<math>\text{9}=\text{3}\centerdot \text{3}=\text{3}^{\text{2}}</math>, hence
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<math>\sqrt{\left( -3 \right)^{2}}=\sqrt{9}=9^{{1}/{2}\;}=\left( 3^{2} \right)^{{1}/{2}\;}=3^{2\centerdot \frac{1}{2}}=3^{1}=3</math>
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NOTE:
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The calculation
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<math>\sqrt{\left( -3 \right)^{2}}=\left( \left( -3 \right)^{2} \right)^{{1}/{2}\;}=\left( -3 \right)^{2\centerdot \frac{1}{2}}=\left( -3 \right)^{1}=-3</math>
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is wrong at the second equals sign. Remember that the power rules apply when the base is positive.

Revision as of 10:44, 22 September 2008

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


\displaystyle \sqrt{\left( -3 \right)^{2}}=\sqrt{9}=9^{{1}/{2}\;}=\left( 3^{2} \right)^{{1}/{2}\;}=3^{2\centerdot \frac{1}{2}}=3^{1}=3


NOTE: The calculation \displaystyle \sqrt{\left( -3 \right)^{2}}=\left( \left( -3 \right)^{2} \right)^{{1}/{2}\;}=\left( -3 \right)^{2\centerdot \frac{1}{2}}=\left( -3 \right)^{1}=-3

is wrong at the second equals sign. Remember that the power rules apply when the base is positive.

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