Prove that 2 route3 -7 is an irrational number?
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let us assume it is a rational number.
so, it is = p/q
2 root3 - 7 =p/q
2 root3 = p/q + 7 (do LCM)
2 root3 = p + 7q/q
root3 = p + 7q/2q
root3 = irrational #
p + 7q/2q = rational # (contains integer)
but, rational # not equal to irrational #
hence proved ........ Q.E.D
so, it is = p/q
2 root3 - 7 =p/q
2 root3 = p/q + 7 (do LCM)
2 root3 = p + 7q/q
root3 = p + 7q/2q
root3 = irrational #
p + 7q/2q = rational # (contains integer)
but, rational # not equal to irrational #
hence proved ........ Q.E.D
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