Question 126399
{{{sqrt(8)*sqrt(250)}}} Start with the given expression



{{{sqrt(8*250)}}} Combine the roots. Remember, {{{sqrt(a)*sqrt(b)=sqrt(a*b)}}}



{{{sqrt(2000)}}} Multiply




Now let's simplify this 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 2000



Factors:

1, 2, 4, 5, 8, 10, 16, 20, 25, 40, 50, 80, 100, 125, 200, 250, 400, 500, 1000, 2000



Notice how 400 is the largest perfect square, so lets factor 2000 into 400*5



{{{sqrt(400*5)}}} Factor 2000 into 400*5
 

{{{sqrt(400)*sqrt(5)}}} Break up the square roots using the identity {{{sqrt(x*y)=sqrt(x)*sqrt(y)}}}

 
{{{20*sqrt(5)}}} Take the square root of the perfect square 400 to get 20 
 



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Answer


So the expression {{{sqrt(8)*sqrt(250)}}} simplifies to {{{20*sqrt(5)}}}




In other words, {{{sqrt(8)*sqrt(250)=20*sqrt(5)}}}