Solution 3.1:4a

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The decimal number
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<center> [[Image:3_1_4a.gif]] </center>
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<math>0.\text{16 }</math>
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can also be written as
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<math>\text{16}\centerdot \text{1}0^{-\text{2}}\text{ }</math>
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and then it is easier to see that, since
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<math>\text{16}=\text{4}\centerdot \text{4}=\text{4}^{\text{2}}\text{ }</math>
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and
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<math>10^{-2}=\left( 10^{-1} \right)^{2}=0.1^{2}</math>
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<math>\begin{align}
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& \sqrt{0.16}=\sqrt{16\centerdot 10^{-2}}=\sqrt{16}\centerdot \sqrt{10^{-2}}=\sqrt{4^{2}}\centerdot \sqrt{0.1^{2}} \\
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& =4\centerdot 0.1=0.4 \\
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\end{align}</math>
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Another alternative is, of course, to see directly that
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<math>0.16=0.4\centerdot 0.4=0.4^{2}</math>, and then that
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<math>\sqrt{0.16}=\sqrt{0.4^{2}}=0.4</math>

Revision as of 13:50, 22 September 2008

The decimal number \displaystyle 0.\text{16 } can also be written as \displaystyle \text{16}\centerdot \text{1}0^{-\text{2}}\text{ } and then it is easier to see that, since \displaystyle \text{16}=\text{4}\centerdot \text{4}=\text{4}^{\text{2}}\text{ } and \displaystyle 10^{-2}=\left( 10^{-1} \right)^{2}=0.1^{2}


\displaystyle \begin{align} & \sqrt{0.16}=\sqrt{16\centerdot 10^{-2}}=\sqrt{16}\centerdot \sqrt{10^{-2}}=\sqrt{4^{2}}\centerdot \sqrt{0.1^{2}} \\ & =4\centerdot 0.1=0.4 \\ \end{align}


Another alternative is, of course, to see directly that \displaystyle 0.16=0.4\centerdot 0.4=0.4^{2}, and then that \displaystyle \sqrt{0.16}=\sqrt{0.4^{2}}=0.4

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