Question 112386
Given:
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{{{sqrt(12) - sqrt(75)}}}
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Factor each of the terms under the radical signs to get:
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{{{sqrt(4*3) - sqrt(25*3)}}}
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Recognize that the square root of a product of terms is equal to the product of the square
roots of each of the terms. Applying this rule results in:
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{{{sqrt(4*3) - sqrt(25*3)= sqrt(4)*sqrt(3) - sqrt(25)*sqrt(3)}}}
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But {{{sqrt(4) = 2}}} and {{{sqrt(25) = 5}}}. Make these substitutions and you get:
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{{{sqrt(4*3) - sqrt(25*3) = 2*sqrt(3) - 5*sqrt(3)}}}
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Factoring {{{sqrt(3)}}} from each of the terms on the right side gives:
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{{{sqrt(4*3) - sqrt(25*3) = (2 - 5)sqrt(3)}}}
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The terms 2 and -5 inside the parentheses combine to -3 and when this is substituted
for the parentheses the problem finally reduces to:
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{{{sqrt(4*3) - sqrt(25*3) = -3*sqrt(3)}}}
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So the answer to this problem is {{{-3*sqrt(3)}}}
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Hope this helps you to understand the problem and how to proceed to solve it.
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