SOLUTION: what is the sqrt of 30,875?

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Question 151532: what is the sqrt of 30,875?
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

sqrt%2830875%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. When you take the square root of this perfect square, you will get a rational number.


So let's list the factors of 30875


Factors:
1, 5, 13, 19, 25, 65, 95, 125, 247, 325, 475, 1235, 1625, 2375, 6175, 30875


Notice how 25 is the largest perfect square, so lets factor 30875 into 25*1235


sqrt%2825%2A1235%29 Factor 30875 into 25*1235


sqrt%2825%29%2Asqrt%281235%29 Break up the square roots using the identity sqrt%28x%2Ay%29=sqrt%28x%29%2Asqrt%28y%29



5%2Asqrt%281235%29 Take the square root of the perfect square 25 to get 5



So the expression sqrt%2830875%29 simplifies to 5%2Asqrt%281235%29


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Check:

Notice if we evaluate the square root of 30875 with a calculator we get


sqrt%2830875%29=175.712833908056


and if we evaluate 5%2Asqrt%281235%29 we get


5%2Asqrt%281235%29=175.712833908056


This shows that sqrt%2830875%29=5%2Asqrt%281235%29. So this verifies our answer