Question

prove that the following are irrational
(1). 1√2​

Answer 1

Answer:

first suppose 1√2 is rational number

then

when 1√2 is rational number then it is form in p by q and q does not equal to 0

p by q =1√2

q=1√2p

q doesn't equal to zero

so

1√2 is irrational number

Answer 2

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prove that the following are irrational,

$\sf{1) \: \: \: \huge\frac{1}{ \sqrt{2} }}$

$\boxed {{༆ \: \pinkⒶ \orangeⓃ \blueⓈ \redⓌ \purpleⒺ \greenⓇ \: ࿐}}$

$\huge \sf{\frac{1}{ \sqrt{2} } = \frac{a}{b} }$

$\huge \sf{ \sqrt{2} = \frac{b}{a} }$

$\sf{ \implies \: But \: \: \sqrt{2} \: \: is \: irrational}$

$\implies \sf{Rational \: \cancel = \: Irrational}$

$\sf \: hence \: \: \huge\frac{1}{ \sqrt{2} } \small \: \: \: is \: irrational$

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