Question

6/3√2 is rational or irrational​

Answer 1

Answer:

6 + 3√2 is irrational number

__________ [PROVE]

Solution:

• Let us assume that 6 + 3√2 is irrational number.

=> 6 + 3√2 = \dfrac{a}{b}

b

a

Here, a and b are co-prime numbers.

=> 3√2 = \dfrac{a}{b}

b

a

- 6

=> 3√2 = \dfrac{a\:-\:6b}{b}

b

a−6b

=> √2 = \dfrac{a\:-\:6b}{3b}

3b

a−6b

Here;

\dfrac{a\:-\:6b}{3b}

3b

a−6b

is rational number.

So, √2 is also a rational number.

But we know that √2 is irrational number.

So, our assumption is wrong.

6 + 3√2 is irrational number.

Hence, proved.

Answer 2

Answer:

6/3√2 is irrational​