Question

`(3)/(sqrt(5))` irrational prove​

Answer 1

GIVEN:

• 3√5

TO FIND:

• Prove that 3√5 is an irrational number

SOLUTION:

Let us assume, to the contrary, that 3√5 is rational. Then, there exist co-prime positive integers a and b such that

$\rm{\dashrightarrow 3\sqrt{5} = \dfrac{a}{b}}$

$\rm{\dashrightarrow \sqrt{5} = \dfrac{a}{3b}}$

$\bf{\dashrightarrow \sqrt{5} \: is \: rational}$ [ ∵ 3, a and b are integers ∴ a/3b is a rational number]

This contradicts this fact that √5 is irrational.

So,

Our assumption is not correct.

Hence, 3√5 is an irrational number.

______________________

✯ Extra Information ✯

➜ Euclid's Division Algorithm = If a and b are positive integers such that a = bq + r, then every common divisor of a and b is a common divisor of b and r , and vice- versa.