Question

prove that root 5 minus 3 root 2 is an irrational number
please answer fast please....

Answer 1

to prove that 5-3√2  is an irrational number:

Assume that 5-3√2 is a rational number

i.e. 5-3 √2 = p/q (p and q are integers, q ≠0 , p and q are co-primes)

Now take all the rational no. from R.H.S and L.H.S to 1 side

5/1-p/q = 3√2

5q-p/q = 3√2 (i.e 3*√2)

5q – p/3q = √2

Since p and q are integers (rational no.) ,5q – p/3q  should also be a rational no.

But √2 is irrational

Which contradicts our assumption is wrong

Therefore 5-3√2  is an irrational no.

Answer 2

Answer:

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