Question

Provr that 2root3 by 5 id an irrantionl number

Answer 1

Let 2root 3 / 5 be a rational no. in the form a/b where, a and b are integers.

Now,

2root3 / 5 = a / b

2root3 = 5a / b

root3 = 5a / 2b

Here. since a/b is a rational no., so 5a / 2b is also a rational no.

Hereby, root3 should also be a rational no.

 

But this contradicts tha fact that root3 is a rational no.

So, our assumption is wrong and hence 2root3 / 5 is an irrational no.

Ishan Goyal answered this

let 2 root3 /5 be a rational no.

then , 2 root3 /5 = a/b

2 root3 b = 5a

a = 2 root3 b /5

on squaring on both side,

a^2 = 12 /25 b^2

this shows that 12/25 can divide a and a^2

therefore it contradicts our assumtion and 2 root3 / 5 is irrational.

Answer 2

Let 2root 3 / 5 be a rational no. in the form a/b where, a and b are integers.

Now,

2root3 / 5 = a / b

2root3 = 5a / b

root3 = 5a / 2b

Here. since a/b is a rational no., so 5a / 2b is also a rational no.

Hereby, root3 should also be a rational no.

But this contradicts tha fact that root3 is a rational no.

So, our assumption is wrong and hence 2root3 / 5 is an irrational no.

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