(1) Where a and b are integers having no common factor (b`0) on squaring both side (3)2= (a/b)2 3= a2/b2 equation (2) 3b2=a2 equation (3) Where a and b are both odd number and a/b reduce to smallest possible terms. It is not possible that a and b are even because if a and b are even one can always be divided by 2 as we assume a/b is an rational numbers a=2m+1 Assuming a and b are odd b=2n+1 by putting the value of a and b in eq 3 : 3(2n+1)2= (2m+1)2 3(4n2+1+4n)= (2m2+1+4m) 12n2+3+12n=4m2+1+4m 12n2+12n+2=4m2+4m 6n2+6n+1=2m2+2m 6n2+6n+1=2(m2+n) In this equation all the value of m is always odd and the value of n is always n for all values s so this equation has no solution. Our assumption a and b are odd in invalid so we can say that root of 3 is an irrational number. In above articles we discuss about how to solve irrational numbers. What are irrational Numbers Irrational numbers are the numbers which are not rational numbers. In other words we can say that any number that cannot be expressed in the form of p/q are termed as irrational numbers. If any floating point number (that is a number that has an integer part as well as an decimal part is termed as floating point number.) cannot expressed as the ratio of two integers that floating point number is termed as irrational numbers. Let us take some of the examples of Irrational numbers Now if we take the value of “ pi (π ) “ that is π = 3.1415926535897932384626433832795 This value of π is Read More About Rational Numbers Properties Worksheets
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Published on Apr 4, 2012
Know More About Worksheet on Scientific Notation and Rational Number Now, we discuss on some equation to solve the irrational number. We ass...