Show that square root of blank end root7 -  3 is irrational

Asked by gpnkumar0 | 5th Sep, 2016, 08:55: PM

Expert Answer:

begin mathsize 12px style To space prove colon space square root of 7 minus 3 space is space irrational
Suppose space square root of 7 minus 3 space is space rational rightwards double arrow square root of 7 minus 3 equals straight p over straight q space where space straight p comma space straight q space are space integers space and space straight q not equal to 0
So comma space square root of 7 minus 3 equals straight p over straight q rightwards double arrow square root of 7 equals straight p over straight q plus 3 equals fraction numerator straight p plus 3 over denominator straight q end fraction
But space we space know space that space square root of 7 space is space irrational comma space so space has space to space be space fraction numerator straight p plus 3 over denominator straight q end fraction space irrational.
But space since space straight p space and space straight q space are space integers comma space fraction numerator straight p plus 3 over denominator straight q end fraction space is space rational.
This space is space straight a space contradiction. space So comma space our space assumption space that space square root of 7 minus 3 space is space rational space is space false.
Hence comma space square root of 7 minus 3 space is space irrational. end style

Answered by Rebecca Fernandes | 5th Sep, 2016, 10:22: PM