Solution 3.1:2e

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Looking first at
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<center> [[Image:3_1_2e.gif]] </center>
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<math>\sqrt{18}</math>
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this square root expression can be simplified by writing
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<math>\text{18}</math>
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as a product of its smallest possible integer factors
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<math>18=2\centerdot 9=2\centerdot 3\centerdot 3=2\centerdot 3^{2}</math>
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and then we can take the quadratic out of the square root sign by using the rule
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<math>\sqrt{a^{2}b}=a\sqrt{b}</math>,
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<math>\sqrt{18}=\sqrt{2\centerdot 3^{2}}=3\sqrt{2}</math>
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In the same way, we write
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<math>8=2\centerdot 4=2\centerdot 2\centerdot 2=2^{3}</math>
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and get
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<math>\sqrt{8}=\sqrt{2\centerdot 2^{2}}=2\sqrt{2}</math>
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All together, we get
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<math>\begin{align}
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& \sqrt{18}\sqrt{8}=3\sqrt{2}\centerdot 2\sqrt{2}=3\centerdot 2\centerdot \left( \sqrt{2} \right)^{2} \\
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& =3\centerdot 2\centerdot 2=12 \\
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& \\
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\end{align}</math>

Revision as of 11:01, 22 September 2008

Looking first at \displaystyle \sqrt{18} this square root expression can be simplified by writing \displaystyle \text{18} as a product of its smallest possible integer factors


\displaystyle 18=2\centerdot 9=2\centerdot 3\centerdot 3=2\centerdot 3^{2}


and then we can take the quadratic out of the square root sign by using the rule \displaystyle \sqrt{a^{2}b}=a\sqrt{b},


\displaystyle \sqrt{18}=\sqrt{2\centerdot 3^{2}}=3\sqrt{2}

In the same way, we write \displaystyle 8=2\centerdot 4=2\centerdot 2\centerdot 2=2^{3} and get


\displaystyle \sqrt{8}=\sqrt{2\centerdot 2^{2}}=2\sqrt{2}


All together, we get


\displaystyle \begin{align} & \sqrt{18}\sqrt{8}=3\sqrt{2}\centerdot 2\sqrt{2}=3\centerdot 2\centerdot \left( \sqrt{2} \right)^{2} \\ & =3\centerdot 2\centerdot 2=12 \\ & \\ \end{align}

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