SOLUTION: Solve 12 + square root of 108 OVER 6

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

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

Start with the expression

First lets reduce
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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

Factor 108 into 36*3

Break up the square roots using the identity

Take the square root of the perfect square 36 to get 6

So the expression

simplifies to

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Simplify the square root (using the technique above)

Break up the fraction

Divide to get

Divide to get

So the expression

simplifies to

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