Question

5√2,Prove that given number is irrational.

Answer 1

Hi ,

Let us assume to the contrary , that

5√2 is rational .

So , we can find coprime integers a and

b ( b ≠ 0 ) such that

5√2 = a/b

√2 = a/5b

Since , a and B are integers , a/5b is

rational , and so , √2 is rational .

But this contradicts the fact that √2 is

irrational .

So , we conclude that 5√2 is irrational.

I hope this helps you.

: )

Answer 2

Hello,

Such type of prove can be done by theory of conflict.

As we already prove that square root of all prime numbers are irrational.

So,we know that √2 is irrational,but we don't know on multiplying with 5, number would become rational or irrational.

Let us assume that 5√2 is rational,so it can be represented in the form of p/q ,where p and q are co-prime numbers and q is not equal to zero.

$5 \sqrt{2} = \frac{p}{q} \\ \\ \sqrt{2} = \frac{p}{5q}$
so,√2 equal to p/q form,which is not possible,so there is a conflict due to our wrong assumption.

Thus 5√2 is irrational number.

Hope it helps you