Question 531134
Given to simplify:
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{{{5*sqrt(18)}}}
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Replace 18 by its equivalent 9 times 2 and you have:
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{{{5*sqrt(9*2)}}}
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But the square root of this product is equal to the product of the square roots. This becomes:
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{{{5*sqrt(9*2) = 5*sqrt(9)*sqrt(2)}}}
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But the square root of 9 is 3. Replace the square root of 9 with 3 and the term is:
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{{{5*3*sqrt(2)}}}
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Multiply the 5 and the 3 and the result is:
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{{{15*sqrt(2)}}}
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The critical part comes from the rule:
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{{{sqrt(a*b) = sqrt(a)*sqrt(b)}}}
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For this problem you can verify this rule by using a calculator to find the square root of 18 (which is equal to the square root of (9*2). Then find the square root of 9 (answer 3) and multiply it by the square root of 2. This product should equal the square root of 18. You will find that it does. This does not prove the rule, but it should give you some confidence that the rule does work.
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Hope this helps you with the problem.
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