Tham khảo tài liệu 'new sat math workbook episode 1 part 9', ngoại ngữ, ngữ pháp tiếng anh phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | Roots and Radicals 145 1. ADDITION AND SUBTRACTION OF RADICALS The conditions under which radicals can be added or subtracted are much the same as the conditions for letters in an algebraic expression. The radicals act as a label or unit and must therefore be exactly the same. In adding or subtracting we add or subtract the coefficients or rational parts and carry the radical along as a label which does not change. Example 5 2 4i cannot be added 5 2 32 cannot be added W2 5 2 9-V2 Often when radicals to be added or subtracted are not the same simplification of one or more radicals will make them the same. To simplify a radical we remove any perfect square factors from underneath the radical sign. Example a 12 44-5 3 2 3 5 27 5 9 -V3 35 3 If we wish to add a 12 V27 we must first simplify each one. Adding the simplified radicals gives a sum of s 3 . Example 125 v 20 -J 500 Solution V25-45 44-45-410445 s 5 245 -105 5 - 5 146 Chapter 10 Exercise 1 Work out each problem. Circle the letter that appears before your answer. 1. Combine 45 27 - 25 48 5 187 A 275 3 B -35 3 C 95 3 D 105 3 E 115 3 2. Combine 780 745 -720 4. Combine 1 -7 180 1 -5 45 - 2 -5 20 A 35 10 5 15 25 2 B 5 C 797 D 24J5 A B C D E 95 5 55 5 -5 5 35 5 -25 5 E none of these 5. Combine 5 mn - 3yfmn - 2y mn 3. Combine 65 5 2 - 45 5 5 2 A 8 B 25 5 35 2 C 25 5 45 2 D 577 E 5 A B C D E 0 1 -jmn mn -simn Roots and Radicals 147 2. MULTIPLICATION AND DIVISION OF RADICALS In multiplication and division we again treat the radicals as we would treat letters in an algebraic expression. They are factors and must be treated as such. Example V2-43 46 Example W2 - s 3 20-46 Example 342Ý 342 - 342 9 - 2 18 Example 4 2 V2 Example 1 2 W5 2 J4 Example 42h 8 W18 416 V36 4 6 10 Exercise 2 Work out each problem. Circle the letter that appears before your answer. 1. Multiply and simplify 2ạ ĩ8. ộựĩ A 72 B 48 C 1246 D 846 E 36 2. Find 343 3 A 2743 B 8h ã C 81 D 943 E 243 3. Multiply and simplify .
