1. Rationalize the binomial aa + ¿§.

Since n = 6, an even number, we have from (2),

a2b‡ + a3⁄4b} — ab + a‡b‡ — b§) — a3 — 13,

=

The foregoing methods may be applied in the solution of the following

13. Find the factor which will rationalize √5 – √2.

281. A Radical Equation is one in which the unknown quantity is affected by the radical sign.

282. In order to solve a radical equation, it is necessary in the first place to rationalize the terms containing the unknown quantity. In case of fractional terms, this may be effected in part by methods already explained. But the process is commonly one of involution.

The following are examples of simple equations containing radical quantities.

1. Given √x + 11 + √√x − 4 5 to find x.

=

The least common multiple of the denominators is x -α= (√x + √a)(√x−√a); and the solution will be as in the following

From these illustrations, we derive the following precepts for the solution of radical equations:

1. It is sometimes advantageous to rationalize the denominator of a fractional term, before transposition or involution.

2. An equation should be simplified as much as possible before involution; and care should be taken so to dispose the terms in the two members as to secure the simplest results after involution

Find the values of the unknown quantity in each of the following equations: