what is the least rationalizing factor of 5 square root of 2.Why cant the least rationalizing factor be 1/root2 or 1/(any large number x root 2).In books it is given root2.
As per defination,rationalizing factor are the ones which should give you a rational number when multiplied with irrational(or surd).

Asked by saif | 4th May, 2017, 08:42: AM

Expert Answer:

begin mathsize 16px style Rationalising space factor space of space open parentheses straight a plus square root of straight b close parentheses space is space always space straight a minus square root of straight b.
as space open parentheses straight a plus square root of straight b close parentheses open parentheses straight a minus square root of straight b close parentheses equals straight a squared minus straight b. space
For space the space 5 square root of 2 space equals 0 plus 5 square root of 2
Rationalising space factor space is space 0 minus 5 square root of 2 equals negative 5 square root of 2
Then space least space rationalising space factor space is space always space square root of 2 space
as space to space get space rational space number space we space have space to space multiply space by space straight a space surd. end style

Answered by Sneha shidid | 4th May, 2017, 10:39: AM