Nhich sum contradicts this statement? The sum of two irrational numbers is always irrational. A sqrt (7)+5sqrt (7) B sqrt (4)+2sqrt (9) C -2sqrt (6)+sqrt (8) D -4sqrt (6)+4sqrt (6)

The statement "The sum of two irrational numbers is always irrational" is not always true. There are cases where the sum of two irrational numbers can be rational.<br /><br />Let's analyze each option:<br /><br />A. $\sqrt{7} + 5\sqrt{7}$<br /> - Both $\sqrt{7}$ and $5\sqrt{7}$ are irrational numbers.<br /> - The sum is $6\sqrt{7}$, which is still an irrational number.<br /> - This option does not contradict the statement.<br /><br />B. $\sqrt{4} + 2\sqrt{9}$<br /> - $\sqrt{4} = 2$ and $2\sqrt{9} = 6$, both of which are rational numbers.<br /> - The sum is $2 + 6 = 8$, which is a rational number.<br /> - This option contradicts the statement.<br /><br />C. $-2\sqrt{6} + \sqrt{8}$<br /> - Both $-2\sqrt{6}$ and $\sqrt{8}$ are irrational numbers.<br /> - The sum is $-2\sqrt{6} + 2\sqrt{2}$, which is still an irrational number.<br /> - This option does not contradict the statement.<br /><br />D. $-4\sqrt{6} + 4\sqrt{6}$<br /> - Both $-4\sqrt{6}$ and $4\sqrt{6}$ are irrational numbers.<br /> - The sum is $0$, which is a rational number.<br /> - This option contradicts the statement.<br /><br />Therefore, the sums that contradict the statement "The sum of two irrational numbers is always irrational" are options B and D.