Question

prove that 3-√5 is irrational number​

Answer 1

HEYA ❤️

WE KNOW THAT √5 IS AN IRRATIONAL NUMBER.

IF WE SUBTRACT, ADD, MULTIPLY, DIVIDE A NON ZERO RATIONAL NUMBER TO A IRRATIONAL NUMBER THE RESULT IS ALWAYS IRRATIONAL.

HENCE, 3-√5 IS AN IRRATIONAL NUMBER.

Answer 2

contrary assume that 3-√5 is rational

3-√5 = a/b

(a and b are coprimes)

√5 = 3 - a/b

√5 = 3b - a/b

3b-a/b is rational

√5 is also rational

but it contradicts the fact that √5 is irrational. This arises due to our wrong assumption.

Therefore, 3-√5 is irrational