A
Simplifying Surds
1
Simplify: 50
2
Simplify: 48
3
Simplify, assuming a and b are positive: 12a³b
B
Operations with Surds
4
Simplify: 35 + 45 − 5
5
Expand and simplify: (2 + 3)²
6
Multiply out and simplify: (5 − 6)(5 + 6)
C
Rationalising the Denominator
7
Rationalise the denominator: 486
8
Rationalise the denominator: 32
9
Rationalise the denominator: 42 + 3
10
Simplify:
1x − 2 − 1x + 2
11
Simplify:
xx + y + yx − y
12
Simplify:
a − ba − b − a − ba + b
13
Simplify:
x − xx − 1 + x − 4x + 2
14
Simplify:
1x − x − 1x + x
15
Simplify:
a + ba − b − a − ba + b
16
Simplify:
35 + 2 + 35 − 2
17
Simplify:
53 + 2 + 53 − 2
18
Simplify:
46 + 2 + 46 − 2
Answer Key
A1: 50 = 25 × 2 = 52
A2: 48 = 16 × 3 = 43
A3: 12a³b = 4a² × 3ab = 2a3ab
B1: (3 + 4 − 1)5 = 65
B2: (2 + 3)² = 4 + 43 + 3 = 7 + 43
B3: (5 − 6)(5 + 6) = 25 − 6 = 19
C1: 486 = 48 ÷ 6 = 8 = 22
C2: 32 × 22 = 62
C3: 42 + 3 × 2 − 32 − 3 = 8 − 43(2+√3)(2−√3) = 1 = 8 − 43
C4: common denominator (x−4): numerator (x+2)−(x−2) = 4 → 4x − 4
C5: common denominator x−y: numerator x(x−y) + y(x+y) = x+y → x + yx − y
C6: (a−b) cancels after conjugates: (a+b) − (a−b) = 2b
C7: x−x = x(x−1) so first fraction = x; second × conjugate = x−2 → 2x − 2
C8: common denominator x²−x: numerator (x+x)−(x−x) = 2x → 2xx² − x
C9: common denominator a−b: numerator (a+b)²−(a−b)² = 4ab → 4aba − b
C10: conjugates give (3÷3) each: (5−2) + (5+2) = 25
C11: conjugates give (5÷1) each: 5(3−2) + 5(3+2) = 103
C12: conjugates give (4÷4) each: (6−2) + (6+2) = 26