Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Simplifying Radical Expressions Algebra 1 If b 2 = a, then b is a square root of a. Meaning Positive Square Root Symbol Example Negative Square Root 9 3 9 3 The positive and negative square roots 9 3 Simplifying Radical Expressions Product Property for Radicals ab a b 36 4 9 100 4 25 36 4 9 10 2 5 6 23 Simplifying Radical Expressions Product Property for Radicals 50 25 2 5 2 • 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. x x 14 7 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 Simplify: 45 9 5 3 5 Simplify: 49 x 49 x 7 x Simplify: 52t 4 13t 2 13t Simplify: 12 x x 2 6 x 6 Square root of a variable to an even power = the variable to one-half the power. Simplify: y y 88 44 Square root of a variable to an even power = the variable to one-half the power. Simplify: x x x 12 1 13 x x 12 x 6 x x Simplify: 27 x x 26 13 x x Simplify: 36x 8 6 x 2 6x 4 8 Simplify: 10 49 y 7y 5 Simplify: 45x 6 9x 5 6 3x 3 5 Simplify: 50 y 7 25 y 2 y 6 5y 3 2y Simplify: 48y 9 Simplify: 80 y 16 16 y 5 16 4y 8 5 Simplify: 36x 3 6x x 4 448x y Simplify: 7 4x y 112 y 4 2 2x y 3 6 4 28y 2 x y 2 4 7y 2 3 2 8x y 3 7y • 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. 9 3 • negative square root: the negative square root of 9 is –3 and is shown like 9 3 • radical: the symbol which is read “the square root of a” is called a radical. • 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. 2 • 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. 3 --- 3 is the 25 4 y 3 36 Simplify: y 3 18 Simplify: 2 x 20 x 50 2 2x 10 x 25 2 2 x 5 2 x 5 2 y 6y 9 2 Simplify: y 3 y 3 2 4 x 5 10 Simplify: 4 x 5 2 x 5 10 5 50 y 7 9 Simplify: 25 y 7 2 y 7 8 5 y 7 4 2 y 7