Question 73436
Given:
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{{{2*sqrt(7t)*sqrt(14t)}}}
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Simplify this.
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Let's see if your answer is correct.
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One way to do this is to use the rule: {{{sqrt(a*b) = sqrt(a)*sqrt(b)}}}
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Applying this rule to 7t leads to {{{sqrt(7t) = sqrt(7)*sqrt(t)}}}
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Then apply this rule twice to 14t to get:
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{{{sqrt(14t) = sqrt(2*7)* sqrt(t) = sqrt(2)*sqrt(7)*sqrt(t)}}}
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Now substitute for sqrt(7t) and sqrt(14t) in the original problem to get:
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{{{2*sqrt(7)*sqrt(t)*sqrt(2)*sqrt(7)*sqrt(t)}}}
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In this string we have {{{sqrt(7)*sqrt(7)}}} and that equals {{{7}}}. We also have 
{{{sqrt(t)*sqrt(t)}}} and that equals {{{t}}}. The rest of the terms remain unchanged.
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So, after substituting {{{t}}} and {{{7}}} the problem reduces to:
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{{{2*7*t*sqrt(2)}}}
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which further simplifies to:
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{{{14*t*sqrt(2)}}} 
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You might want to change it to have the variable last. If you do the answer is:
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{{{(14*sqrt(2))*t}}}
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But there's nothing wrong with your answer.  Another good job!