Find two irrational numbers between 2 and 2.5.
Solution:
Let x be an irrational number between 2 and 2.5, therefore,
2<x<2.5[Assumption]⇒22<x<2.52[Takingsquaresandsquareroots]⇒4<x<6.25[∵4and6.25aretwoperfectsquares,thusthesquarerootofallintegresbetweenthemareirrational]∴x=5,6
Final answer: Hence, any two irrational numbers between 2 and 2.5.are 5 and 6.