Roots, Scientific Notation, and Polynomials

Roots and Exponents

A square root asks what value multiplies by itself to produce a given value. The principal square root of a non-negative number is the non-negative value that equals the number when multiplied by itself. The number or expression located under the radical symbol is called the radicand. An integer produced by multiplying an integer by itself is called a perfect square, such as 16, 25, or 36. When working with non-negative numbers a and b, radical multiplication follows the rule √(ab) = √a · √b, and division for a ≥ 0 and b > 0 follows the rule √(a/b) = √a/√b.

To simplify a square root, factor out the largest perfect square factor from the radicand. For example, if the radicand contains a perfect square such as 16, 25, or 36, you factor that value out using the product rule. Like radicals are terms that have the same index and the same radicand after simplification, although their outside coefficients may differ. To combine radicals by addition or subtraction, first simplify them completely, and then combine only like radicals. When adding or subtracting like radicals, combine their outside coefficients and keep the radical factor unchanged.

Exponents and roots share a direct algebraic connection. An exponent of 1/n means taking the nth root; for example, x^(1/2) = √x for x ≥ 0. In a rational exponent m/n, where n is a positive integer, m tells you the power and n tells you the root index. Furthermore, any non-zero base raised to a negative exponent equals 1 divided by the base raised to the positive exponent.

The TI-30XS calculator provides dedicated tools to evaluate radical expressions quickly. On the TI-30XS calculator, the square root function is accessed by pressing the green 2nd button followed by the x-squared key. Knowing this keystroke sequence allows you to input principal square roots accurately during practice and testing.