Question

prove that, this is irrational => 5-√7​

Answer 1

AnSwEr:-

Let us assume that 7√5 is rational number

Let us assume that 7√5 is rational numberHence, 7√5 can be written in the form of a/b where a, b are co-prime and b not equal to 0.

Let us assume that 7√5 is rational numberHence, 7√5 can be written in the form of a/b where a, b are co-prime and b not equal to 0.7√5 = a/b

Let us assume that 7√5 is rational numberHence, 7√5 can be written in the form of a/b where a, b are co-prime and b not equal to 0.7√5 = a/b√5 = a/7b

Let us assume that 7√5 is rational numberHence, 7√5 can be written in the form of a/b where a, b are co-prime and b not equal to 0.7√5 = a/b√5 = a/7bhere √5 is irrational and a/7b is rational number.

Let us assume that 7√5 is rational numberHence, 7√5 can be written in the form of a/b where a, b are co-prime and b not equal to 0.7√5 = a/b√5 = a/7bhere √5 is irrational and a/7b is rational number.Rational number ≠ Irrational number

Let us assume that 7√5 is rational numberHence, 7√5 can be written in the form of a/b where a, b are co-prime and b not equal to 0.7√5 = a/b√5 = a/7bhere √5 is irrational and a/7b is rational number.Rational number ≠ Irrational numberIt is contradiction to our assumption 7√5 is rational number.

Let us assume that 7√5 is rational numberHence, 7√5 can be written in the form of a/b where a, b are co-prime and b not equal to 0.7√5 = a/b√5 = a/7bhere √5 is irrational and a/7b is rational number.Rational number ≠ Irrational numberIt is contradiction to our assumption 7√5 is rational number.Therefore, 7√5 is an irrational number.