Question

The sum of two surds yields a rational number if both surds are equal in and opposite in sign.

• A. magnitude
• B. number
• C. size
• D. shape

Answer 1

The correct option is A magnitude

Sum of two surds will give a rational number only when both are of opposite signs and have same magnitude.
Let's understand it through examples.
Let one surd be $\sqrt{3}$ and another surd be $-\sqrt{3}$
Sum of both surds $=\sqrt{3}+(-\sqrt{3})$
$=\sqrt{3}-\sqrt{3}$
$=0$
Here, sum of both surds is $0$ which is a real number.