Download The product (quotient) of the roots of two numbers is equal to the

4.3 Mixed and Entire Radicals Deduce Rules Involving Radicals Example 1. Determine whether each statement is true or false. a) ___ √9 + √4 is equal to √9
4 b) ___ √9 – √4 is equal to √9
4 c) ___ √9 x √4 is equal to √9x4 d) ___ √9 ÷ √4 is equal to √9
4 The product (quotient) of the roots of two numbers is equal to the root of the product (quotient) of the two numbers. The sum (difference) of the roots of two numbers is NOT equal to the root of the sum (difference) of the two numbers. √ x √ = √ x √ + √ ≠ √
√
√
= √ – √ ≠ √ – Try. State whether each statement is true or false. √
a) ___ √3 x √6 = √18 b) ___ √
= √2 c) ___ √16 + √9 = √16
9 Simplify Radicals Example 2. Write the following as a single radical in the form √ √
a) √8 x √3 b) √
c) √
√
Example 3. Express as a product of radicals. a) √77 b) √27 c) √40 Multiplication Property of Radicals √ = √ ∙ √ , where n is a natural number, and a and b are real numbers. Simplify Radicals Using Prime Factorization Example 4. Simplify each radical. a) √20 b) √144 c) √162 12 Entire Radicals Radicals of the form √ such as √80 , √144 , √162 Mixed Radicals Radicals of the form √ such as 4√5 , 2 √18 , 3 √2 = 1 Improper Mixed Fraction Number Please note there are many ways to simplify a radical but only one of them is correct. 5
√200 √200 √200 = √4 ∙ 50 = √25 ∙ 8 = √100 ∙ 2 = √4∙√50 = √25∙√8 = √100∙√2 = 2√50 = 5√8 = 10√2 Write Radicals in Simplest Form Example 5. Write each radical in simplest form, if possible. a) √40 b) √26 c) √32 Try. Write each radical in simplest form, if possible. a) √30 b) √32 c) √48 Write Mixed Radicals as Entire Radicals Example 6. Write each mixed radical as an entire radical. a) 4√3 b) 3 √2 c) 2 √2 Try. Write each radical in simplest form, if possible. a) 7√3 b) 2 √4 c) 2 √3 Example 7. Arrange the radicals in order from least to greatest without a calculator. 2 √11 , 3 √3 , 4 √2 , 2 √6 13