SOLUTION: Use Property 1 to simplify each of the following radical expressions. Assume that all variables represent positive real numbers. Sqrt108

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Question 109192: Use Property 1 to simplify each of the following radical expressions. Assume that all variables represent positive real numbers.
Sqrt108
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Solved by pluggable solver: Simplifying Square Roots (whole numbers only)
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. When you take the square root of this perfect square, you will get 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 factor 108 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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Check:

Notice if we evaluate the square root of 108 with a calculator we get


sqrt%28108%29=10.3923048454133


and if we evaluate 6%2Asqrt%283%29 we get


6%2Asqrt%283%29=10.3923048454133


This shows that sqrt%28108%29=6%2Asqrt%283%29. So this verifies our answer