While we have discussed the simplification of radical expressions in another article, I think it would be helpful to look at a step-by-step approach at how this can be done. This way, the student can memorize and undertake the relevant simple steps in simplifying the radical expression in an orderly manner. Suppose we have the number 50 under a square root sign:
1) Find a factor of the number that indicates a perfect square. In this case, we have 25. This, multiplied by 2, gives us 50. So we see that the square root of 50 = 25 x 2, keeping in mind that we still have 25 x 2 under a square root sign.
2) Find the square root of the perfect square. The perfect square is 25, and the square root of 25 is 5. At this point, 25 and 2 are each under distinct square root signs.
3) Now that we have found the square root of 25, which is 5, we can take it out from under the square root sign and put it to the left of the square root sign. We are left with 5 x the square root of 2. Thus, we have our answer. It might help the mathematics student to memorize these three simple steps in simplifying radical expressions.