Question 151532


{{{sqrt(30875)}}} 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(25*1235)}}} Factor 30875 into 25*1235


 
{{{sqrt(25)*sqrt(1235)}}} Break up the square roots using the identity {{{sqrt(x*y)=sqrt(x)*sqrt(y)}}}
 
 
 
{{{5*sqrt(1235)}}} Take the square root of the perfect square 25 to get 5 
 
 
 
So the expression {{{sqrt(30875)}}} simplifies to {{{5*sqrt(1235)}}}



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Check:


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



{{{sqrt(30875)=175.712833908056}}}



and if we evaluate {{{5*sqrt(1235)}}} we get



{{{5*sqrt(1235)=175.712833908056}}}



This shows that {{{sqrt(30875)=5*sqrt(1235)}}}. So this verifies our answer