Question

prove that 3-5√3 is an irrational no​

Answer 1

HALLO!

Let 3 - 5√3 be a rational number.

.°. 3- 5√3 = $\frac{p}{q}$ [ where p and q are integer , q ≠ 0 and q and p are co- prime number ]

=> -5√3 = $\frac{p-3}{q}$

=> - 5√3 = $\frac{p-3q}{q}$

=> √3 = $\frac{p-3q}{-5q}$

we know that $\frac{p}{q}$ is a rational number.

.°. √3 is also a rational number.

This contradicts our assumption

3-5√3 is an irrational number

Answer 2

Answer:

Let 3 - 573 be a rational number. ... 3-5V3 = [ where p and q are integer, q= 0 and q and p are co-prime number] => -5V3 = p-3 9 => -5V3 = 2–39 9 => V3 = p–39 -59 we know that ? is a rational number. 9 ..V3 is also a rational number.

This contradicts our assumption 3-5V3 is an irrational number