17. α-8. 19. 3x-2y3. 21. 4x-8y-2. 23.

2a-1x2 3-2b2y-5

abc

26.

a-2bc-2d

a-26

a-16-2-8

α-46-50-6

27.

29.

a-26-20-4

a-16-5-8

If a = 4, b = 2, c = 1, find the numerical value of :

46. ab-2.

5. x 2 + x-ly-1 + y2 by x-2 - x-ly-1 + y-2.

6. x - xy + y by x + ys.

7. 2 + xy + y* by x - yt.

8.1 + b−1 + b 2 by 1 – b−1 + b-2.

9. a + 2a-36 by 26-4a6a-z.

8. 9x

5. x - 3x3 + 3x – 1 by x

x2y + y by x - x + y + yt.

9 x - 12x - 2+4x+x-1 by 3x-2

4

9.2x-2+6x-ly-1 - 16 x2y + by 2x+2x2y-1+4x3y-2.

9x-4-18x-3y+15x-2y-6x-ly+y2|3x-2-3x-1y2 +y

2. 4 α

4a-4az+6.

4x+4.

4. 4α-2+4 a−1 + 1.

5. 9a - 12 a + 10 - 4 a ̄ + a-1.

CHAPTER XVII.

RADICAL EXPRESSIONS.

253. A radical expression is an expression affected by

6

3

the radical sign; as √a, √9, Va, Va + b, √32.

254. An indicated root that cannot be exactly obtained is called a surd. An indicated root that can be exactly obtained is said to have the form of a surd.

The required root shows the order of a surd; and surds are named quadratic, cubic, biquadratic, according as the second, third, or fourth roots are required.

The product of a rational factor and a surd factor is called a mixed surd; as 3√2, b√a. The rational factor of a mixed surd is called the coefficient of the surd.

When there is no rational factor outside of the radical sign, that is, when the coefficient is 1, the surd is said to be entire; as √2, Va.

255. A surd is in its simplest form when the expression under the radical sign is integral and as small as possible. Surds are said to be similar if they have the same surd factor when reduced to the simplest form.

NOTE. In operations with surds, arithmetical numbers contained in the surds should be expressed in their prime factors.

Reduction of Radicals.

256. To reduce a radical is to change its form without changing its value.