1. The music theory teacher explained that a surd is a number that cannot be expressed as a simple fraction.
音乐理论老师解释说，surd 是一个不能表示为简单分数的数字。

2. She struggled to simplify the surd equation without a calculator.
她在没有计算器的情况下努力简化 surd 方程。

3. The surd roots of the equation were difficult to calculate by hand.
这个方程的 surd 根在手算时很难计算。

4. The surd nature of the problem made it challenging for the students to solve.
问题的 surd 特性使学生难以解决。

5. The mathematician specialized in working with surd numbers and irrational quantities.
这位数学家专门研究 surd 数字和无理量。

6. The surd values in the equation required a more advanced understanding of mathematics.
方程中的 surd 值需要更高级的数学理解。