SOLUTION: Can this equation be simplified any further if so can I see step by step how it is done. t = -64+ the radical of 4288 divided by -32

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Question 140637: Can this equation be simplified any further if so can I see step by step how it is done. t = -64+ the radical of 4288 divided by -32
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

Start with the expression
%28-64+%2B+sqrt%284288%29%29%2F-32

First lets reduce sqrt%284288%29
-----------------------------------------------------
sqrt%284288%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 4288
Factors:
1, 2, 4, 8, 16, 32, 64, 67, 134, 268, 536, 1072, 2144, 4288


Notice how 64 is the largest perfect square, so lets break 4288 down into 64*67


sqrt%2864%2A67%29 Factor 4288 into 64*67

sqrt%2864%29%2Asqrt%2867%29 Break up the square roots using the identity sqrt%28x%2Ay%29=sqrt%28x%29%2Asqrt%28y%29

8%2Asqrt%2867%29 Take the square root of the perfect square 64 to get 8

So the expression

sqrt%284288%29

simplifies to

8%2Asqrt%2867%29
-----------------------------------------------------

%28-64+%2B+8%2Asqrt%2867%29%29%2F-32 Simplify the square root (using the technique above)

-64%2F-32+%2B+8%2Asqrt%2867%29%2F-32 Break up the fraction

2+%2B+8%2Asqrt%2867%29%2F-32 Divide -64%2F-32 to get 2

2+-%281%2F4%29%2Asqrt%2867%29 Divide 8%2F-32 to get -1%2F4



So the expression
%28-64+%2B+sqrt%284288%29%29%2F-32

simplifies to

2+-%281%2F4%29%2Asqrt%2867%29