Aim How Do We Simplify Radicals Definitions Finding

Aim: How Do We Simplify Radicals?

Definitions Finding the square root of a given number is the reverse process of squaring a number. radical sign. radicand. The entire expression, including the radical sign and radicand, is called the radical expression.

Definitions The index tells the “root” of the expression. Since square roots have an index of 2, the index is generally not written in a square root. Example:

Definitions Square roots of negative numbers are not real numbers. Square roots of negative numbers are called imaginary numbers. There is no number multiplied by itself that will give you – 25. (Imaginary numbers will be studied later)

Definitions A perfect square is the square of a natural number. 1, 4, 9, 16, 25, and 36 are the first six perfect squares. A rational number is one that can be written in the form, where a and b are integers, and b 0. Real numbers that are not rational numbers are called irrational numbers. As decimals, irrational numbers are nonrepeating, nonterminating decimals.

Perfect Squares • • 1 4 9 16 25 36 49 64 81 100 121 144 169 196 225 256 289 324 400 625

LEAVE IN RADICAL FORM Perfect Square Factor * Other Factor = = = = =

LEAVE IN RADICAL FORM Perfect Square Factor * Other Factor = = = = =

LEAVE IN RADICAL FORM Perfect Square Factor * Other Factor = = = = =

Cube and Fourth Roots is read “the cube root of a. ” is read “the fourth root of a. ”

=X = Y 3 = P 2 X 3 Y = 2 X 2 Y = 5 C 4 D 5