7 - Roots and Radicals

Abstract

This chapter discusses operations on and simplification of radicals. Most of the radical expressions involve square roots. Finding the square root of a number is the reverse of raising a number to the second power. Every positive number has two square roots, one positive and the other negative. The square roots of any number that is not itself a perfect square are irrational numbers. If the negative square root of a number is considered, a negative sign must be put in front of the radical. Negative numbers have square roots, but their square roots are not real numbers. They do not have a place on the real number line. There are many other roots of numbers besides square roots, although square roots seem to be the most commonly used. The cube root of a number is the number raised to the third power to get the original number. With even root such as square roots, fourth roots, sixth roots, and so on, negative numbers cannot be under the radical sign. All variables that appear under a radical sign represent positive numbers. There are many application problems involving radicals that require decimal approximations.