Question 98208
Given:
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{{{sqrt(11)*(sqrt(11) + x*sqrt(22))}}}
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This is a problem involving distributed multiplication. It is of the form:
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{{{A*(B + C) = A*B + A*C}}} <=== call this rule 1
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Notice that you are just multiplying the term outside the parentheses by each of the terms
inside the parentheses.
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What makes this problem a little "different" is that it involves multiplication of square roots,
so you need to know a few rules about those multiplications.  Here are a couple of rules for
square roots:
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{{{sqrt(A)* sqrt(A) = A}}} <=== call this rule 2
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and:
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{{{sqrt(A*B) = sqrt(A)*sqrt(B)}}} <=== call this rule 3
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It seems as if this problem involves a lot of {{{sqrt(11)}}} terms. But notice that there
is one term that is {{{sqrt(22)}}}. If we apply rule 3 to that term, we can get a {{{sqrt(11)}}} 
from it by doing the following:
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{{{sqrt(22) = sqrt(2*11) = sqrt(2)*sqrt(11)}}}
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So in the problem we can replace {{{sqrt(22)}}} by {{{sqrt(2)*sqrt(11)}}} and the problem
then becomes:
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{{{sqrt(11)*(sqrt(11)+ x*sqrt(2)*sqrt(11))}}}
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Now let's apply rule 1. We'll do that by multiplying {{{sqrt(11)}}} times each of the
terms in the parentheses to get:
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{{{sqrt(11)*sqrt(11) + sqrt(11)*x*sqrt(2)*sqrt(11)}}}
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Now we can apply rule 2 to both of these terms. The first term is {{{sqrt(11)*sqrt(11)}}}
and rule 2 tells us that the answer is just 11. So substituting 11 into the problem reduces
the problem to:
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{{{11 + sqrt(11)*x*sqrt(2)*sqrt(11)}}}
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Notice now that in the second term there is also a {{{sqrt(11)*sqrt(11)}}} involved. Rule
2 also allows us to replace that product with 11. And this substitution further reduces the
problem to:
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{{{11 + 11*x*sqrt(2)}}}
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That's the answer to this problem. I suppose that if you wanted to you could factor out
the 11 that is common to both terms to get {{{11*(1 + x*sqrt(2))}}} but that's up to you
and what your instructions are.
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Hope this helps you to understand the problem a little more.