Question

show that (2+root3)(2- root 3)(5+root2 )(5-root2) is a rational number ​

Answer 1

Answer:

$(2 + \sqrt{3} )(2 - \sqrt{3} )(5 + \sqrt{2} )(5 - \sqrt{2} ) \\ = > (2 {}^{2} - ( \sqrt{3} {)}^{2} )(5 {}^{2} - ( \sqrt{2} {}^{2} )) \\ = > (4 - 3)(25 - 2) \\ = > (1)(23) \\ = > 23$

Therefore, 23 is a rational number.