Question

HEY MATE.....

Here is a question...


prove that...
$\frac{1}{ \sqrt{7} }$
Is irrational.....


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Answer 1

To prove : 1 / root ( 7 ) is an irrational number

i.e , To prove :

{ 1 / root ( 7 ) } × { root ( 7 ) / root ( 7 ) } is an irratinal number

i. e , to prove : root ( 7 ) / 7 is an irratinal number

Let if possible suppose , root ( 7 ) / 7 is a rational number...

Now as root ( 7 ) / 7 is a rational number

=> { root ( 7 ) / 7 } × 7 is also a rational number

( product of two rational number is a rational number )

=> ( root ( 7 ) × 7 ) / 7 = root ( 7 )

=> root ( 7 ) is a rational number

but this contradicts the fact that root ( 7 ) is an irrational number ( Note that root ( P ) is an irrational number if P is a prime number )

=> hence our assumption was wrong , Thus 1 / root ( 7 ) is an irrational number..

Answer 2

Answer:

since a and b are integer definitely 1a/b is rational no. also root 7 is also rational no....so 1/root 7 is irrational..... hence proved..