# Lesson RATIONAL AND IRRATIONAL NUMBERS

Algebra ->  Algebra  -> Real-numbers -> Lesson RATIONAL AND IRRATIONAL NUMBERS      Log On

 Ad: Algebrator™ solves your algebra problems and provides step-by-step explanations! Ad: Algebra Solved!™: algebra software solves algebra homework problems with step-by-step help!

 Algebra: Real numbers, Irrational numbers, etc Solvers Lessons Answers archive Quiz In Depth
 This Lesson (RATIONAL AND IRRATIONAL NUMBERS) was created by by psbhowmick(529)  : View Source, ShowAbout psbhowmick: M.Tech. (Aerospace Engineering); If you want paid help for your Math questions then send me email at partha[dot]s[dot]bhowmick[at]gmail[dot]com RATIONAL NUMBER __________________ Any number which be expressed in the form where 'p' and 'q' (q not equal to 1) are integers mutually prime to each other (this means 'p' and 'q' have no common factors; in other words H.C.F. of 'p' and 'q' is 1) is called a rational number. e.g. 56, -235.6, 5/7, , etc Note: . Thus -235.6 can be expressed as a ratio of two integers -1178 and 5 and -1178 and 5 have no factors common between them. IRRATIONAL NUMBER ____________________ Any number which be expressed in the form where 'p' and 'q' ('q' not equal to 1) are integers mutually prime to each other (this means 'p' and 'q' have no common factors; in other words H.C.F. of 'p' and 'q' is 1) is called an irrational number. e.g. , , , etc Note: Let us prove that is an irrational number. Let us assume that is a rational number. Then it can be expressed as where 'p' and 'q' are mutually prime integers and 'q' unequal to 1. Squaring both sides or ______(1) Now, as 'q' is an integer so '5q' is also an integer. But as 'p' and 'q' has no common factors and 'q' is not equal to 1, so cannot be an integer. So, there is a contradiction! Left side of eqn.(1) is an integer but the right side is not. This cannot be true. So our very assumption that is a rational number must be wrong. Hence, is an irrational number. If you have any query regarding this lesson you may send your query to me. Email: partha.s.bhowmick@gmail.com This lesson has been accessed 14333 times.