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203 Rh CHAPTER XXIII.

Surds (Radicals).

227. A surd is an indicated root which cannot be exactly obtained.

Thus 2, 35, 5 a3, a^2 + b^2 are surds.

By reference to the preceding chapter it will be seen that these are only cases of fractional indices; for the above quantities might be written

Since surds may always be expressed as quantities with fractional indices they are subject to the same laws of combination as other algebraic symbols.

228. A surd is sometimes called an irrational quantity; and quantities which are not surds are, for the sake of distinction, termed rational quantities.

229. Surds are sometimes spoken of as radicals. This term is also applied to quantities such as a^2, 9, 3 27, etc., which are, however, rational quantities in surd form.

230. The order of a surd is indicated by the root symbol, or surd index. Thus 3 x, n a are respectively surds of the third and nth. orders.

The surds of the most frequent occurrence are those of the second order ; they are sometimes called quadratic surds. Thus 3, a, x + y are quadratic surds.

231. A mixed surd is one containing a factor whose root can be extracted.