Question

show that
$4 \sqrt{2}$
sho that it is irrational number​

Answer 1

$\small\orange {\sf{Bonjour\ Mate!}}$

☆$\small\green {\sf{Answer }}$☆

Let us assume that 4√2 is a rational number.

Rational numbers can be expressed in the form a/b, where a and b are co - prime and b ≠0

\implies 4\sqrt{2}=\dfrac{a}{b}

\implies \sqrt{2} = \dfrac{a}{4b}

The RHS is a rational number

=> LHS is also a rational number

=> √2 is also a rational number

But this contradicts to the fact that √2 is an irrational number.

Hence, our assumption is wrong.

\boxed{\boxed{\bold{Therefore, \ 4\sqrt{2} \ is \ an \ irrational \ number}}}}}

Answer 2

Answer:

☆\small\green {\sf{Answer }}Answer ☆

Let us assume that 4√2 is a rational number.

Rational numbers can be expressed in the form a/b, where a and b are co - prime and b ≠0

\implies 4\sqrt{2}=\dfrac{a}{b}

\implies \sqrt{2} = \dfrac{a}{4b}

The RHS is a rational number

=> LHS is also a rational number

=> √2 is also a rational number

But this contradicts to the fact that √2 is an irrational number.

Hence, our assumption is wrong.