Surds can occur in algebraic expressions. When a surd involves a fraction, it should not be left with a square root as a denominator. As an example, consider `frac(1)(sqrt(x))`. To remove the `sqrt(x)` as the denominator, multiply the fraction (both numerator and denominator) by `sqrt(x)`, such that:

`frac(1)(sqrt(x)) xx frac(sqrt(x))(sqrt(x)) = frac(sqrt(x))(x)`

The rules for manipulating surds algebraically are the same as those used for manipulating surds arithmetically:

• `sqrt(ab) = sqrt(a) xx sqrt(b)` (multiplying two surds);

• `msqrt(a) + nsqrt(a) = (m + n)sqrt(a)` (adding two like surds);

• `sqrt(frac(a)(b))` = `frac(√a)(√b)` (dividing two surds).