Question 207332
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 252



Factors:

1, 2, 3, 4, 6, 7, 9, 12, 14, 18, 21, 28, 36, 42, 63, 84, 126, 252



Notice how 36 is the largest perfect square, so lets factor 252 into 36*7



{{{sqrt(252)}}} Start with the given expression



{{{sqrt(36*7)}}} Factor 252 into 36*7
 
 
 
{{{sqrt(36)*sqrt(7)}}} Break up the square roots using the identity {{{sqrt(x*y)=sqrt(x)*sqrt(y)}}}
 
 
 
{{{6*sqrt(7)}}} Take the square root of the perfect square 36 to get 6 
 
 
 
So the expression {{{sqrt(252)}}} simplifies to {{{6*sqrt(7)}}}



In other words, {{{sqrt(252)=6*sqrt(7)}}}