CHAPTER XXI.

MULTIPLICATION OF RADICALS.

229. Since by (214) ava × Vb = aab, it follows that radicals of a common index may be multiplied together as integers, and the result placed under a radical with the common index, the product of the coefficient being prefixed.

× (a2 — b2) × √a + b × √ a − b × √a2 — b2,

(6) Multiply:

a √a-√b

a2√b-b2 Va

a3Vaba2√b2

- ab2√a2 + b2√ab

a3√aba2√b2 — ab2√a2 + b2√ab

=(a3 + 12)√ab — a2b — a2b2.

Since

CHAPTER XXII.

DIVISION OF RADICALS.

aab = aa × ŵb,

we have, by (214), aVabaab.

230. Hence, it follows that one radical may be divided by another, if both are of common index, by dividing the coefficient of the divisor into the coefficient of the dividend for the coefficient of the quotient, and the surd factor of the divisor into the surd factor of the dividend for the surd factor of the quotient.

(3) Divide a√b - b√a by √ab.

Dividing each term of the dividend separately, we have,

TO RATIONALIZE THE DIVISOR.

231. This method is employed when the divisor is a compound expression. Also when it is desired to find the approximate numerical value of one surd divided by another.

Multiplying both terms by √5, we rationalize the divisor, and have,

(2) Divide 2+3√2 by 2-3√2.

Multiplying both dividend and divisor by 2+3√2, we have,