(27)

pr+(pq+qr)x+q2x2 ̧ ̧ps+(pt−qs)x — qtx2

X

p-qx

p+qx

CIV.

SURDS.

1. Reduce to their simplest forms-
(1) (3/a2+3/ab+3⁄4/b2) (3⁄4/a−3/b).
(2) (2√32—3√2+4)+8.

2. (1) Square (a+b√−1)*+(a−b√=1)}.

(2) Extract the square root of 31 — 12√✓ −5.

(3) 7√45+2/180+11/245.

(4) 23/4x32/54.

(5) (x*—xy3+x3y—y3)+(x*—y3).

4. (1) Show that if x+√ÿ=a+√b, x=a, y=b, and apply the principle to determine the square root of 12-4√5.

(2) (√5−√2) (√2+1) (√3+√2) (√2−1).

10. Square 32-2√7, and extract the square root of

(7) √128-32+√/8-√√/16.

(8) √5.3/2.44.

12. (1) Prove that

{√3+4√=I+√/8—4√=1}2=

(2) Simplify 7+4√3+√7−4√3.

=16.

(6) Divide x+y+z-33⁄4/xyz by x3+y3+23.

15. If √ ax+√by+ √cz=0, show that

a2x2+b2y2+c2z2=2(abxy+acxz+boyz).

(1) x*+xy ̄1—2x+y ̄*—2x3y‡+2x+y$+y.

9xy=20(x+y); 10xz=24(x+z); 11yz=30(y+z).

7.

8.

9.

3x=2y and a3=y3.

10.

√x2+ay-b2=c+x l

√y2+mx=x+y