Question

prove 2-4√7 is irrational​

Answer 1

$\huge \pink {prove√}$

Assume that 4-2√7 is an rational number

=> 4-2√7 = p/q

Squaring both sides

=> 16 + 2/7 - 4√7 = p²/q²

=> - 4√7 = p²/q² - 16 - 2/7

=> √7 = (p²/q² - 16 - 2/7)/-4

=> √7 = (16 + 2/7 -p²/q² )/4

=> √7 = 4 + 2/8 - p²/4q²

RHS = Rational

LHS = irrational ( as given that ✓7 is an irrational number)

=> LHS ≠ RHS

Hence our assumption is wrong

Hence 4-2√7 is not an rational number

=> 4-2√7 is irrational number