Simplifying Radical Expressions Algebra 1 If b 2

Simplifying Radical Expressions Algebra 1

If b 2 = a, then b is a square root of a. Meaning Symbol Example Positive Square Root Negative Square Root The positive and negative square roots

Simplifying Radical Expressions

Simplifying Radical Expressions • A radical has been simplified when its radicand contains no perfect square factors. • Test to see if it can be divided by 4, then 9, then 25, then 49, etc. • Sometimes factoring the radicand using the “tree” is helpful.

Steps 1. Try to divide the radicand into a perfect square for numbers 2. If there is an exponent make it even by using rules of exponents 3. Separate the factors to its own square root 4. Simplify

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Simplify: Square root of a variable to an even power = the variable to one -half the power.

Simplify: Square root of a variable to an even power = the variable to one -half the power.

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Terminology: • square root: one of two equal factors of a given number. The radicand is like the “area” of a square and the simplified answer is the length of the side of the squares. • Principal square root: the positive square root of a number; the principal square root of 9 is 3. • negative square root: the negative square root of 9 is – 3 and is shown like • radical: the symbol • radicand: the number or expression inside a radical symbol radicand. • perfect square: a number that is the square of an integer. 1, 4, 9, 16, 25, 36, etc… are perfect squares. • irrational number: a number whose decimal form is nonterminating and nonrepeating. • Rational number: a number that can be written in the form a/b, where a and b are integers (b cannot equal 0) • radical expression: an expression that contains a radical. which is read “the square root of a” is called a radical. --- 3 is the

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