SOLUTION: how do you reduce -4+sq.root of 40/-2

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Question 120455This question is from textbook
: how do you reduce -4+sq.root of 40/-2 This question is from textbook

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

Start with the expression
%28-4+%2B+sqrt%2840%29%29%2F-2

First lets reduce sqrt%2840%29
-----------------------------------------------------
sqrt%2840%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 40
Factors:
1, 2, 4, 5, 8, 10, 20, 40


Notice how 4 is the largest perfect square, so lets break 40 down into 4*10


sqrt%284%2A10%29 Factor 40 into 4*10

sqrt%284%29%2Asqrt%2810%29 Break up the square roots using the identity sqrt%28x%2Ay%29=sqrt%28x%29%2Asqrt%28y%29

2%2Asqrt%2810%29 Take the square root of the perfect square 4 to get 2

So the expression

sqrt%2840%29

simplifies to

2%2Asqrt%2810%29
-----------------------------------------------------

%28-4+%2B+2%2Asqrt%2810%29%29%2F-2 Simplify the square root (using the technique above)

-4%2F-2+%2B+2%2Asqrt%2810%29%2F-2 Break up the fraction

2+%2B+2%2Asqrt%2810%29%2F-2 Divide -4%2F-2 to get 2

2+%2B+-1%2Asqrt%2810%29 Divide 2%2F-2 to get -1


2-sqrt%2810%29 Multiply



So the expression
%28-4+%2B+sqrt%2840%29%29%2F-2

simplifies to

2-sqrt%2810%29