SOLUTION: Solve 12 + square root of 108 OVER 6

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Question 119793: Solve
12 + square root of 108 OVER 6

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

Start with the expression
%2812+%2B+sqrt%28108%29%29%2F6

First lets reduce sqrt%28108%29
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sqrt%28108%29 Start with the given expression
The goal of simplifying expressions with square roots is to factor the radicand into a product of two numbers. One of these two numbers must be a perfect square. This way the perfect square will become a rational number.
So let's list the factors of 108
Factors:
1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 108


Notice how 36 is the largest perfect square, so lets break 108 down into 36*3


sqrt%2836%2A3%29 Factor 108 into 36*3

sqrt%2836%29%2Asqrt%283%29 Break up the square roots using the identity sqrt%28x%2Ay%29=sqrt%28x%29%2Asqrt%28y%29

6%2Asqrt%283%29 Take the square root of the perfect square 36 to get 6

So the expression

sqrt%28108%29

simplifies to

6%2Asqrt%283%29
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%2812+%2B+6%2Asqrt%283%29%29%2F6 Simplify the square root (using the technique above)

12%2F6+%2B+6%2Asqrt%283%29%2F6 Break up the fraction

2+%2B+6%2Asqrt%283%29%2F6 Divide 12%2F6 to get 2

2+%2B+1%2Asqrt%283%29 Divide 6%2F6 to get 1



So the expression
%2812+%2B+sqrt%28108%29%29%2F6

simplifies to

2+%2B+sqrt%283%29