tailieunhanh - Master the Gre 2010 - Part 26

Peterson's Master the Gre 2010 - Part book includes 9 full-length practice tests , thorough reviews of every section on the exam, and expert tips and strategies from a test prep pro. GRE (Graduage Record Examination General Test) is a commercially-run standardized test and an admission requirement for many graduate schools in USA and other English-speaking countries. GRE can earn you between 200-800 points. | Chapter 10 Math Review Number Theory and Algebra 233 MULTIPLICATION AND DIVISION Terms under different radicals can be combined under a common radical if one term is multiplied or divided by the other. But if the radicals are different for example square root and cube root combining terms is a bit tricky as in the last example below. X X X o x y X x 5 X 5 1 1 2 X5 6 14. 2 2a 2 5 A 4 a B 4a2 C 8a D 8a2 E 6a The correct answer is C . Square each of the two terms 2 and 2a separately. Then combine their squares by multiplication 2 2a 2 22 X 2a 2 4 X 2a 8a. Roots You Should Know For the GRE memorize the roots in the following table. If you encounter one of these radical terms on the exam chances are you ll need to know its equivalent integer to answer the question. In the table notice that the cube root of a negative number is negative and the cube root of a positive number is positive. 234 PART IV Quantitative Reasoning Square Roots of Perfect Square Integers Cube Roots of Perfect Cube Integers Positive and Negative 2 8 - 2 2 27 - 3 2 64 - 4 - 125 - 5 - 216 - 6 - 343 - 7 - 512 - 8 - 729 - 9 - 1 000 - 10 Roots and the Real Number Line As with exponents the root of a number can bear a surprising relationship to the magnitude and or sign negative vs. positive of the number. This is another of the test makers favorite areas. Here are three rules you should remember If n 1 then 1 n n n the greater the root the lesser the value . .3 n n 1 the greater the root the greater the value . n 64 1 64 64 64 1 4 8 64 The square root or other even-number root of any negative number is an imaginary number not a real number. That s why the preceding rules don t cover these roots. Q Every negative number has exactly one cube root and that root is a negative number. The same holds true for all other odd-numbered roots of negative numbers. - 27 23 -3 -3 -3 -27 -2 -2 -2 -2 -2 -2 -32 Chapter 10 Math Review Number Theory and Algebra 235 Q Every positive .