Prove Square Root of 3 is Irrational Prove Square Root of 3 is Irrational
Here I am telling you the best way of understanding that root of 3 is an irrational number. Prove square root of 3 is Irrational can be solved in the below mention manner. So we are assuming √3 is a rational number i.e √3=a/b equation (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 equation 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 so this equation has no solution. Know More About Worksheets of Rational Numbers in Expressions
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