Question

Prove that 1/√2 ia an Irrational.​

Answer 1

Question :–

Prove that $\sf \dfrac{1}{ \sqrt{2}}$ is an Irrational.

Prove :–

$\implies \sf \dfrac{1}{ \sqrt{2}} \times \sf \dfrac{\sqrt{2}}{\sqrt{2}}$

$\implies \sf \dfrac{\sqrt{2}}{{(\sqrt{2})}^{2}}$

$\implies \sf \dfrac{ \sqrt{2}}{2}$

We know that √2 is an IR (Irrational) & if IR (Irrational) divided by any integers it becomes IR (Irrational) again.

Hence, $\sf \dfrac{\sqrt{2}}{ \sqrt{2}}$ is an IR (Irrational)

i.e. $\sf \dfrac{1}{ \sqrt{2}}$ is an IR (Irrational)