SOLUTION: Divide. Rationalize the denominator if necessary. Then simplify. 6- the square root of 20 OVER 2

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Question 118070: Divide. Rationalize the denominator if necessary. Then simplify.
6- the square root of 20 OVER 2
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

Start with the expression
%286+-+sqrt%2820%29%29%2F2

First lets reduce sqrt%2820%29
-----------------------------------------------------
sqrt%2820%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 20
Factors:
1, 2, 4, 5, 10, 20


Notice how 4 is the largest perfect square, so lets break 20 down into 4*5


sqrt%284%2A5%29 Factor 20 into 4*5

sqrt%284%29%2Asqrt%285%29 Break up the square roots using the identity sqrt%28x%2Ay%29=sqrt%28x%29%2Asqrt%28y%29

2%2Asqrt%285%29 Take the square root of the perfect square 4 to get 2

So the expression

sqrt%2820%29

simplifies to

2%2Asqrt%285%29
-----------------------------------------------------

%286+-+2%2Asqrt%285%29%29%2F2 Simplify the square root (using the technique above)

6%2F2+-+2%2Asqrt%285%29%2F2 Break up the fraction

3+-+2%2Asqrt%285%29%2F2 Divide 6%2F2 to get 3

3+-+1%2Asqrt%285%29 Divide 2%2F2 to get 1



So the expression
%286+-+sqrt%2820%29%29%2F2

simplifies to

3+-+sqrt%285%29