Page:Elementary algebra (1896).djvu/199

EVOLUTION. 181 EXAMPLES XXI. c.

Find the square root of each of the following expressions

1. 2o 7. ^-«!-a + l. 64 8 2. 3. y y 4r y 8. 9. 10. - 3 a3 + 2^ + 04 _ 5 ^ .|. 6 7^2. 4. y- 2 ax «2 y" by l/ 11. 4 :>: a-- a^ 5. ^y' Sy ^ 12. ^ 2^^ + 3-^ ^+1. 2 2 16 6. 25 " ' 9:c^ 13. 4 3 9 3 14. ^«^ a:2 6 5 101 25 4:k 15 a 4r.2^ 9«2 15. Wm^ + J^?n2,i + 8 m^ + |n2 + |;i + l. 16. 4x*+32x2 + 96+ — + ^.

201. The Cube Root of Any Multinomial. Since the cube of a + 6 is a' + 3rt-6 + Sab- + 6^, we have to discover a process by which a and b, the terms of the root, can be found when a^ + 3 a^5 + 3 ab- + b^ is given.

The first term a is the cube root of a3.

Arrange the terms according to powers of one letter a; then the first term is a3, and its cube root a. Set this down as the first term of the required root. Subtract a^ from the given expression, and the remainder is

3aVj --3ab- + b^ or (3a- + Sab + 6^) x 6.

Now the first term of the remainder is the product of 3 a^ and b. Thus to obtain b we divide the first term of the remainder by three times the square of the term already found.

Having found b we can complete the divisor, which consists of the following three terms;