Question 340427


{{{sqrt(3087)}}} 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(441*7)}}} Factor 3087 into 441*7
 

{{{sqrt(441)*sqrt(7)}}} Break up the square roots using the identity {{{sqrt(x*y)=sqrt(x)*sqrt(y)}}}
 

{{{21*sqrt(7)}}} Take the square root of the perfect square 441 to get 21 
 

So the expression {{{sqrt(3087)}}} simplifies to {{{21*sqrt(7)}}}


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Check:

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


{{{sqrt(3087)=55.5607775323564}}}


and if we evaluate {{{21*sqrt(7)}}} we get


{{{21*sqrt(7)=55.5607775323564}}}


This shows that {{{sqrt(3087)=21*sqrt(7)}}}. So this verifies our answer 



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Jim