Question

prove that 4√5/7
is an irrational number

Answer 1

let us assume 4✓5/7 as a rational number.

→ 4✓5/7 = a/b where a and b are Co-primes.

4✓5/7 = a/b

or , 4✓5 = 7a/b

or, ✓5 = 7a/4b

→ ✓5 = 7a/4b but this contradicts the fact that √5 is irrational.

Hence , a contradiction has arisen due to our wrong assumption of 4✓5/7 as rational.

→ 4√5/7 is Irrational.
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