Forms of Real Numbers

Numbers that lie between integers on the number line can be written as decimal numbers. These consist of an integer part, a decimal point as a separator, and a non-zero decimal part written to the right of the decimal point. Consider the number 12.346 as an example. The integer part of this number is 12. Since there is a decimal part, 0.346, the number is greater than 12 but less than 13. Therefore, when plotting 12.346 on a number line, the point will lie between 12 and 13. It is important to note that these decimals can have very different values, depending on their place value.

The n^(th) root of a real number a expresses another real number that, when multiplied by itself n times, will result in a. In addition to the radical symbol, the notation is made up of the radicand a and the index n. The resulting number is commonly called a radical. For example, the radical expression sqrt(16) is the fourth root of 16. Notice that sqrt(16) simplifies to 2 because 2 multiplied by itself 4 times equals 16. sqrt(16) = sqrt(2^4) = 2 The general expression sqrt(a) represents a number which equals a when multiplied by itself n times.

For any real number a and natural number n, the expression a^(1n) is defined as the n^(th) root of a. Note that a root with an even index is defined only for non-negative numbers. Therefore, if n is even, then a must be non-negative. Just as with exponents, the most common roots have special names: square roots and cube roots have an index of 2 and 3, respectively.