SOLUTION: use property 1 to simplify the following radical expressions. assume that all variables represent positive real numbers /50

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Question 96817: use property 1 to simplify the following radical expressions. assume that all variables represent positive real numbers
/50
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%2850%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 50

Factors:

1, 2, 5, 10, 25, 50



Notice how 25 is the largest perfect square, so lets factor 50 into 25*2





sqrt%2825%2A2%29 Factor 50 into 25*2



sqrt%2825%29%2Asqrt%282%29 Break up the square roots using the identity sqrt%28x%2Ay%29=sqrt%28x%29%2Asqrt%28y%29



5%2Asqrt%282%29 Take the square root of the perfect square 25 to get 5



So the expression sqrt%2850%29 simplifies to 5%2Asqrt%282%29



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Check:

Notice if we evaluate the square root of 50 with a calculator we get


sqrt%2850%29=7.07106781186548


and if we evaluate 5%2Asqrt%282%29 we get


5%2Asqrt%282%29=7.07106781186548


This shows that sqrt%2850%29=5%2Asqrt%282%29. So this verifies our answer