Question

Prove that 3 root 7 is irrational number?

Answer 1

Given : 3√7

To Find : prove that  its irrational number

Solution:

Lets assume that  3√7 is not irrational number

Hence its a rational number

so  3√7 can be written as p/q  where p & q are co prime

3√7 = p/q

=> p  = 3√7q

Squaring both sides

=> p²  = 9 * 7 q²

As on left side its  a square and 7 is a prime number

Hence  q must of form 7n

q = 7n

=> p² = 9 * 7 (7n)²

=> p² = 9 * 7 * 7².n²

=> p must of form 7m

it means p & q must have a common factor 7

so o & q are not co prime

so our initial assumption that  3√7 is rational is wrong

Hence  3√7 is irrational

QED

Hence proved

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