Question

prove that root ∛5 is an irrational number.

Answer 1

Step-by-step explanation:

let us assume ,to the contrary ,that

$3 \sqrt{5}$ is rational.

Then,there exist co-prime integers a and b (not =to 0) such that ,

$3 \sqrt{5} = a \div \: b$

=>

$\sqrt{5} = a \div 3b$

since, a and b are integers ,we get a÷3b is rational ,so

$\sqrt{5}$

is irrational

$\sqrt[3]{5} \: is \: irrational$