Question

proof that root7 is a irrational

Answer 1

We can prove √7 an irrational by contradiction method :
Let us assume that √7 is a rational number
Therefore, √7 = p/q , where p and q have no common factor
Squaring both sides
7 = p^2/q^2
7/p^2 = q^2 ..........(1)
Since p^2 is divisible by 7
So 7 is a factor of p^2
Thus 7 is a factor of p
Now, put p^2 = m in (1)
7m = q^2
m = q^2/7
Since q^2 is divisible by 7
So, 7 is also a factor of q^2
Thus, 7 is a factor of q
But, it contradicts the fact that p and q have no common factor
Therefore, our assumption is wrong
Therefore √7 is an irrational.
Hence Proved.
Hope helped

Answer 2

Answer:

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