SOLUTION: Simplify. Express your answer in simplied radical form. sqrt 250

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Question 89101: Simplify. Express your answer in simplied radical form.
sqrt 250
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
sqrt%28250%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 250
Factors:
1, 2, 5, 10, 25, 50, 125,


Notice how 25 is the largest perfect square, so lets break 250 down into 25*10


sqrt%2825%2A10%29 Factor 250 into 25*10

sqrt%2825%29%2Asqrt%2810%29 Break up the square roots using the identity sqrt%28x%2Ay%29=sqrt%28x%29%2Asqrt%28y%29

5%2Asqrt%2810%29 Take the square root of the perfect square 25 to get 5

So the expression

sqrt%28250%29

simplifies to

5%2Asqrt%2810%29