In Algebra I, you learned about perfect square numbers and how to simplify the square roots of numbers that are not perfect squares. For example: Are 16 and 324 are perfect squares?

A perfect square is a number whose square root is an integer (i.e., a positive or negative whole number or zero). So, based on this definition, 16 is a perfect square, since its principal square root is 4, an integer. Similarly, 324 is a perfect square, since its principal square root is 18, another integer.

On the other hand, 50 is not a perfect square, as there is no integer that is the square root of 50. Try 7: 7 times 7 is 49. Try the next greater integer, 8: 8 times 8 is 64.

For those real numbers that are not perfect squares, we may be able to express them in a simpler form. Again, consider 50. The calculator tells us that the is an irrational number that begins as 7.071067812 (before the calculator screen runs out of space!). An approximation of this square root, obtained by rounding the decimal, is 7.07. But this is merely an approximation: when you determine in the calculator, you get 49.9849.

As you learned in Algebra I, a better way to express is to leave it in radical form, but simplify the radical: . Since 2 is a prime number, and is itself an irrational number, is the most simplified, yet wholly accurate representation of . In the next topic, you will extend your skills of simplifying square roots to other roots (nth roots) of terms containing rational numbers and variables.