15. a√x3-b√x3у3+c√x1Ã3 by abc√x3y.

16. 21 axyz-7 axу√xz +14 a√22 by 7 a√z.

CHAPTER XXIII.

INVOLUTION AND EVOLUTION OF RADICALS.

232. The power or the root of a radical may be found by using fractional exponents.

233. The product or quotient of two quadratic surds which have not the same irrational part will be irrational.

For

and

√xy × √xz = √x2yz=x√ÿz, x √yz÷ X2= √xy.

234. One quadratic surd cannot be the sum or the difference of two others which have not the same irrational part.

That is, a surd equals a rational number, which is impossible.
In the equation a ±V
√b = x±√y, a = x and √b=√y.
If a does not equal x, suppose it equals x ± m.

235. The square root of a binomial, one of whose terms is a quadratic surd and the other rational, may sometimes be expressed by a binomial, one or both terms of which may be a quadratic surd. Let a + √ be the given binomial, and let its square root be expressed by Vx+√y.