use eculid's division lemma to show that the sq of any positive integer is either of the form 3m or 3m+1for some integer m... (b) prove that √7is irrational.(c)show that 5-√3 is an irrational no.
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A.by using Euclid division lemma
a=bq+r
3m=(3 k)square =9k=3(3k)=3m
{let (3k)be m}
3m+1= (3 k+1)square =(9k+3k+1)=3(3k+1)+1=3m+l
a=bq+r
3m=(3 k)square =9k=3(3k)=3m
{let (3k)be m}
3m+1= (3 k+1)square =(9k+3k+1)=3(3k+1)+1=3m+l
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