SOLUTION: I need a little help solving this expression. Simplify {{{(50+sqrt125)/5}}}

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Question 103977: I need a little help solving this expression. Simplify
%2850%2Bsqrt125%29%2F5
Found 2 solutions by jim_thompson5910, MathLover1:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

Start with the expression
%2850+%2B+sqrt%28125%29%29%2F5

First lets reduce sqrt%28125%29
-----------------------------------------------------
sqrt%28125%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 125
Factors:
1, 5, 25, 125


Notice how 25 is the largest perfect square, so lets break 125 down into 25*5


sqrt%2825%2A5%29 Factor 125 into 25*5

sqrt%2825%29%2Asqrt%285%29 Break up the square roots using the identity sqrt%28x%2Ay%29=sqrt%28x%29%2Asqrt%28y%29

5%2Asqrt%285%29 Take the square root of the perfect square 25 to get 5

So the expression

sqrt%28125%29

simplifies to

5%2Asqrt%285%29
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%2850+%2B+5%2Asqrt%285%29%29%2F5 Simplify the square root (using the technique above)

50%2F5+%2B+5%2Asqrt%285%29%2F5 Break up the fraction

10+%2B+5%2Asqrt%285%29%2F5 Divide 50%2F5 to get 10

10+%2B+1%2Asqrt%285%29 Divide 5%2F5 to get 1



So the expression
%2850+%2B+sqrt%28125%29%29%2F5

simplifies to

10+%2B+sqrt%285%29

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
%2850%2Bsqrt%28125%29%29%2F5
%2850%2Bsqrt%285%2A25%29%29%2F5 now we have: sqrt%2825%29=5, take it out of sqrt, and we will have
%2850%2B+5sqrt%285%29%29%2F5 now divide by 5 both nominator and denominator, and you will have
%2810%2Bsqrt%285%29%29