SOLUTION: "How do you simplify the radical, square root of 250"

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Question 207330: "How do you simplify the radical, square root of 250"
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
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. When you take the square root of this perfect square, you will get a rational number.


So let's list the factors of 250


Factors:
1, 2, 5, 10, 25, 50, 125, 250


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


sqrt%28250%29 Start with the given expression


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


In other words, sqrt%28250%29=5%2Asqrt%2810%29