MATHEMATICS
ALGEBRA
Finding the Square Root of a Radical
Square root problems stump many mathematics students. Of course, everyone knows the easy ones, like:
sqrt (25) = 5
sqrt (81) =9
Things get a bit trickier when you throw a variable into the mix.
Consider the following:
sqrt (12x3)
This requires you to more than just input memorized square roots. The solution is fairly simply, though, if you can work methodically.
The first step is to reduce each factor as far as you can:
12 = 4 * 3
12 = 2 * 2 * 3
x = x * x * x
The next step is pull out like pairs. These pairs will fall outside the square root sign in the final solution. In the above problem, you have a pair of 2’s, and a pair of x’s. These become the first part of the solution:
2x
Then you have the x and the 3 which are left over. You can’t reduce 3 any further; nor can you reduce x any further. So these will stay within the square root sign in the final solution. Here is the simplified version of sqrt (12x3):
2x sqrt(3x)