Question

Which of the following is true about like surds?

• A. Like surds have same surd - factor.
• B. Like surds can be reduced to have same surd factor.
• C. Like surds cannot be reduced to same surd factor.
• D. None of the above

Answer 1

Answer: (A), (B)

Like surds can be reduced to have same surd factor.
Like surds have same surd - factor.

$7\sqrt{2}$ and $3\sqrt{2}$ are like surds because both contain $\sqrt{2}$.

$7\sqrt{2}$ and $3\sqrt{8}$ are also like surds because $3\sqrt{8}=3\sqrt{2\times 2\times 2}=6\sqrt{2}$ contain radical $\sqrt{2}$. It can be inferred that like surds can be reduced to same surd factor.

Hence, options A and B are correct.