SOLUTION: Simplify and combine like radicals √ 12 - √ 75

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Question 112386: Simplify and combine like radicals
√ 12 - √ 75
Answer by bucky(2189) About Me  (Show Source):
You can put this solution on YOUR website!
Given:
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sqrt%2812%29+-+sqrt%2875%29
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Factor each of the terms under the radical signs to get:
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sqrt%284%2A3%29+-+sqrt%2825%2A3%29
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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%284%2A3%29+-+sqrt%2825%2A3%29=+sqrt%284%29%2Asqrt%283%29+-+sqrt%2825%29%2Asqrt%283%29
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But sqrt%284%29+=+2 and sqrt%2825%29+=+5. Make these substitutions and you get:
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sqrt%284%2A3%29+-+sqrt%2825%2A3%29+=+2%2Asqrt%283%29+-+5%2Asqrt%283%29
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Factoring sqrt%283%29 from each of the terms on the right side gives:
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sqrt%284%2A3%29+-+sqrt%2825%2A3%29+=+%282+-+5%29sqrt%283%29
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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%284%2A3%29+-+sqrt%2825%2A3%29+=+-3%2Asqrt%283%29
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So the answer to this problem is -3%2Asqrt%283%29
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Hope this helps you to understand the problem and how to proceed to solve it.
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