Question

Prove that 12 under root 3 -41 is an irational number solution

Answer 1

if possible , let 12√3-41 is rational
=> 12√3-41 +41 is also rational [ sum of rationals is rational]
=> 12√3
=>1/12×12√3 is also rational [ product of rationals is rational ]
=>√3 is also rational

but this contradicts the fact that √3 is irrational ,our assumption is wrong
hence,12√3-41 is an irrational number .

Answer 2

Answer:

Let us assume that 12√3-41 is rational no.

i.e. 12√3-41 = a/b

=> 12√3 = a/b +41

=> 12√3 = a+41b/b

=> √3 = a+41b/12b

=> a+41b/12b is rational number..

But, √3 is irrational number.

Thus, this contradicts our assumption

.°. 12√3-41 is irrational number.

Hence proved...

HOPE IT HELPED...☺️