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Radicals, such as , arise from reversing the process of squaring a number. That is, they are inverse operations. Table 2-1 shows you the results of squaring the first five positive integers and then taking the square root (radical) of the result.

TABLE 2-1 Squaring and Taking a Square Root (Radical) Are Inverse Operations

Squares	Square Roots (Radicals)

When you understand how to place radicals such as , , and so forth on the number line, you can see how other values such as , , and so on also fit in. Figure 2-1 shows you a number line that includes specified values of radicals.

FIGURE 2-1: Radicals on the number line.

Notice that radicals of square numbers are always equivalent to integers. In contrast, radicals like and are irrational numbers that fit between these integers on the number line.

When you see this ordered relationship, you can estimate the value of a radical by finding the two integer values where it must fit on the number line. For example:

Where on the number line does the value of occur?

(A) Between 4 and 5

(B) Between 5 and 6

(C) Between 6 and 7

(D) Between 7 and 8

The number 39 falls on the number line between the square numbers 36 and 49. Therefore, falls between and , so Answer C is correct.