please answer 7,8 .please give pic.of solved answer
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Let us assume that 7 is rational. Then, there exist co-prime positive integers a and b such that
7=ba
⟹a=b7
Squaring on both sides, we get
a²=7b²
Therefore, a2 is divisible by 7 and hence, a is also divisible by 7
so, we can write a=7p, for some integer p.
Substituting for a, we get 49p²=7b²⟹b²=7p².
This means, b² is also divisible by 7 and so, b is also divisible by 7.
Therefore, a and b have at least one common factor, i.e., 7.
But, this contradicts the fact that a and b are co-prime.
Thus, our supposition is wrong.
Hence, 7 is irrational.
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