Question

show that 5√3 is an irrational number​

Answer 1

Here's the answer mate......

Answer 2

Answer:

5 is not a irrational number so, 5√3 will be a irrational number if √3 is a irrational number.

If possible let us think √3 is a rational number

∴ √3 = p/q [where p and q is two integers without any common factor and q ≠ 0]

clearly, 1<3<4 so, √1<√2<√3 so, 1<p/q<2

if n=1 then 1<m<2 which  is not possible because there is no integers between 1 and 2

∴ q≠1 and q>1

√3 = p/q so, 3 = p²/q² so, 3q = p²/q

as 3 and q both are integers then, 3n will be a integer.

now, q>1 and there is no common factor between p and q so, there is no common factor between p² and q which shows that p²/q is not a integer and which is against imagination so, √3 is a irrational number.