Question

prove that √2 =(2/√2)

Answer 1

$\large{hey \: mate \: here \: is \: your \: answer}$

$\textbf{Given.. To Prove }$

$\sqrt{2} = \frac{2}{ \sqrt{2} }$

$\textbf{Proof...}$

Here We need To prove √2 = 2√2

Here ,

LHS = √2 ---- EQ. [ 1 ]

RHS = 2 /√2

For Proving This First We Need Take Either LHS or RHS And Simplify It And Show RHS = LHS ..

So Now The Side Which Can Be Simplified Is RHS

So Taking RHS We Have ➡️

RHS = 2 /√2

And Now We Need To Simplify This

So For That First We can Rationalize Denominator ( 2 / √2 )

That is ➡️

$\frac{2}{ \sqrt{2} } = \frac{2}{ \sqrt{2} } \times \frac{ \sqrt{2} }{ \sqrt{2} }$

That is ➡️

$\frac{2 \sqrt{2} }{ { (\sqrt{2}) }^{2} } ( \: as \: \: a \: \times a = {a}^{2} )$

So Now We Have

$\frac{2 \sqrt{2} }{2} ( \: \sqrt{a} \times \sqrt{a} = { (\sqrt{a} \: ) }^{2} = a$

So Now Cancelling 2 From Both Numerator And Denominator We Have....

$\frac{ \sqrt{2} }{1}$

That Is ....

$\sqrt{2} \: \: \: eq \: - - - - \: \: (2)$

Hence The Simplified Form Of RHS Is ..

$\sqrt{2}$

$\textbf{Now From EQ 1 and 2 We Have}$

LHS = RHS

That is ➡️

√2 = 2/√2

$\huge{Hence Proved !!!}$

# Be Brainly .....