Question 89101
{{{sqrt(250)}}} 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. This way the perfect square will become a rational number.

So let's list the factors of 250

Factors:

1, 2, 5, 10, 25, 50, 125,



Notice how 25 is the largest perfect square, so lets break 250 down into 25*10



{{{sqrt(25*10)}}} Factor 250 into 25*10
 
{{{sqrt(25)*sqrt(10)}}} Break up the square roots using the identity {{{sqrt(x*y)=sqrt(x)*sqrt(y)}}}
 
{{{5*sqrt(10)}}} Take the square root of the perfect square 25 to get 5 
 
So the expression


{{{sqrt(250)}}}


simplifies to


{{{5*sqrt(10)}}}