SOLUTION: "how do you simplify the radical, square root of 252"

Algebra ->  Radicals -> SOLUTION: "how do you simplify the radical, square root of 252"      Log On


   

Question 207332: "how do you simplify the radical, square root of 252"
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
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%28252%29 Start with the given expression


sqrt%2836%2A7%29 Factor 252 into 36*7



sqrt%2836%29%2Asqrt%287%29 Break up the square roots using the identity sqrt%28x%2Ay%29=sqrt%28x%29%2Asqrt%28y%29



6%2Asqrt%287%29 Take the square root of the perfect square 36 to get 6



So the expression sqrt%28252%29 simplifies to 6%2Asqrt%287%29


In other words, sqrt%28252%29=6%2Asqrt%287%29