Question

How will you show this (✓2)^2 is equal to 2 ?​

Answer 1

${( \sqrt{2}) }^{2} = 2$

As,

$\sqrt{2} = {2}^{ \frac{1}{2} } \\ \\ Now, \\ \: \: \: \: \: \: \: \: \: \: \: \: { ({2}^{ \frac{1}{2} } )}^{2} \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: {2}^{ \frac{1}{2} \times 2 } \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: {2}^{ \frac{2}{2} } = {2}^{1} = 2$

PROVED !!!