SOLUTION: What is the simplified radical form of 3087? I factored this number by three two times but I am stuck on 343 becuase I don't know what numbers it is divisible by. 3087

Algebra ->  Radicals -> SOLUTION: What is the simplified radical form of 3087? I factored this number by three two times but I am stuck on 343 becuase I don't know what numbers it is divisible by. 3087       Log On


   

Question 340427: What is the simplified radical form of 3087?
I factored this number by three two times but I am stuck on 343 becuase I don't know what numbers it is divisible by.
3087
3 1029
3 343

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

sqrt%283087%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 3087


Factors:
1, 3, 7, 9, 21, 49, 63, 147, 343, 441, 1029, 3087


Notice how 441 is the largest perfect square, so lets factor 3087 into 441*7


sqrt%28441%2A7%29 Factor 3087 into 441*7

sqrt%28441%29%2Asqrt%287%29 Break up the square roots using the identity sqrt%28x%2Ay%29=sqrt%28x%29%2Asqrt%28y%29

21%2Asqrt%287%29 Take the square root of the perfect square 441 to get 21

So the expression sqrt%283087%29 simplifies to 21%2Asqrt%287%29

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Check:
Notice if we evaluate the square root of 3087 with a calculator we get

sqrt%283087%29=55.5607775323564

and if we evaluate 21%2Asqrt%287%29 we get

21%2Asqrt%287%29=55.5607775323564

This shows that sqrt%283087%29=21%2Asqrt%287%29. So this verifies our answer


If you need more help, email me at jim_thompson5910@hotmail.com

Also, feel free to check out my tutoring website

Jim