Question

Which of the following will result in a rational number?​

• A. $7\sqrt{5}-2\sqrt{5}$
• B. $4\sqrt{3}\times (-2\sqrt{12})$
• C. $4\sqrt{7}+\sqrt{7}$
• D. $9\sqrt{6}÷3\sqrt{2}$

Answer 1

The correct option is B $4\sqrt{3}\times (-2\sqrt{12})$

• $7\sqrt{5}-2\sqrt{5}=5\sqrt{5}$, which is an irrational number.


• $4\sqrt{3}\times (-2\sqrt{12})$ $=4\sqrt{3}\times -2\times 2\sqrt{3}$$=4\sqrt{3}\times -4\sqrt{3}=16\times -3$ $=-48$, which is a rational number.


• $4\sqrt{7}+\sqrt{7}=5\sqrt{7}$, which is an irrational number.


• $9\sqrt{6}÷3\sqrt{2}=9\sqrt{2}\sqrt{3}÷3\sqrt{2}$$=3\sqrt{3}$, which is an irrational number.