2) Each problem carries 4 marks.4x4=1610. a) Prove that rootn is not a

1.	2) Each problem carries 4 marks.4x4=1610. a) Prove that rootn is not a rational number, if n is not a perfect square.
Answer» Let , us assume that √n is rational . so, √n = a/b where a and b are integers and b is not equation to zero . Let, a/b are co- prime taking square both side ,we get => n = a^2/b^2=> nb^2 = a^2 ......(1)so, n divide a^2 it means n also divide a for some integer ca = nc now squaring both side a^2 = n^2c^2=> nb^2 = n^2c^2 [ from (1) ]=> b^2 = nc^2 so , n divide b^2 it means b also divide b so, a and b have n as a prime factor but this contradict the fact that a and b are co- prime . therefore , our assumption is wrong .hence, √n is irrational Like my answer if you find it useful!

2) Each problem carries 4 marks.4x4=1610. a) Prove that rootn is not a rational number, if n is not a perfect square.

Answer»

Let , us assume that √n is rational .

so, √n = a/b where a and b are integers and b is not equation to zero .

Let, a/b are co- prime taking square both side ,we get

=> n = a^2/b^2=> nb^2 = a^2 ......(1)so, n divide a^2 it means n also divide a for some integer ca = nc

now squaring both side a^2 = n^2c^2=> nb^2 = n^2c^2 [ from (1) ]=> b^2 = nc^2

so , n divide b^2

it means b also divide b

so, a and b have n as a prime factor

but this contradict the fact that a and b are co- prime .

therefore , our assumption is wrong .hence, √n is irrational

Like my answer if you find it useful!