Question

(3+ √2)(2-√3)(3-√2)(2+√3) is a rational num?

Answer 1

Answer:

NO IT IS NOT A RATIONAL NUMBER

AS √2*√3=√6

Answer 2

Answer:

$(3+ √2)(2-√3)(3-√2)(2+√3) \\ = {(3)}^{2} - {( \sqrt{2}) }^{2} \times {(2)}^{2} - {( \sqrt{3}) }^{2} \\ (identity \: (a + b) \times (a - b) = {a}^{2} - {b}^{2} ) \\ = 9 - 2 \times 4 - 3 \\ = 7 \times 1 \\ = 7$

Hence, (3+ √2)(2-√3)(3-√2)(2+√3) is a rational number.