Question 116380
You are given:
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{{{sqrt(50) + sqrt(18)}}}
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To simplify this you can use the rule that says:
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{{{sqrt(A*B) = sqrt(A)*sqrt(B)}}}
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Applying that rule to {{{sqrt(50)}}} we can break the 50 up into the product of 25*2.
So we can say that {{{sqrt(50) = sqrt(25*2) = sqrt(25)*sqrt(2)}}}
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But {{{sqrt(25) = 5}}}. So we can substitute 5 for {{{sqrt(25)}}} and the problem simplifies
further:
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{{{sqrt(50) = sqrt(25*2) = sqrt(25)*sqrt(2) = 5*sqrt(2)}}}
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Now let's do the same thing for {{{sqrt(18)}}}. Factor 18 so that you have:
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{{{sqrt(18) = sqrt(9*2) = sqrt(9)* sqrt(2)}}}
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And {{{sqrt(9) = 3}}} so this part of the problem simplifies further to:
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{{{sqrt(18) = sqrt(9*2) = sqrt(9)* sqrt(2) = 3*sqrt(2)}}}
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Put the two parts of the problem together ...
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{{{sqrt(50) + sqrt(18) = 5*sqrt(2) + 3*sqrt(2)}}}
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If you factor {{{sqrt(2)}}} from the two terms on the right side you get:
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{{{5*sqrt(2) + 3*sqrt(2) = (5 + 3)*sqrt(2) = 8*sqrt(2)}}}
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So the answer to this problem is:
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{{{sqrt(50) + sqrt(18) = 8*sqrt(2)}}}
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Hope this helps you to understand one of the rules that can be used in simplifying 
radicals.
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