Question 1:
Simplify the following expressions:
1(a) 2(\sqrt{5})
ANSWER: Multiple Choice (Type 1)
A: 2\sqrt{5}
B: \sqrt{10}
C: \sqrt{7}
D: \sqrt{3}
Workings: 2(\sqrt{5}) = 2\times \sqrt{5} = 2\sqrt{5}
Marks = 1
1(b) \sqrt{7} \times \sqrt{7}
ANSWER: Multiple Choice (Type 1)
A: 2\sqrt{7}
B: 7
C: 77
D: \sqrt{77}
Workings: \sqrt{7} \times \sqrt{7} = 7
Marks = 1
1(c) \sqrt{11} ^2
ANSWER: Multiple Choice (Type 1)
A: 2\sqrt{11}
B: 11
C: 121
D: 11\sqrt{11}
Workings: \sqrt{11} ^2 = \sqrt{11} \times \sqrt{11} = 11
Marks = 1
1(d) \sqrt{8} \times \sqrt{2}
ANSWER: Multiple Choice (Type 1)
A: \sqrt{10}
B: \sqrt{14}
C: 4
D: 16
Workings: \sqrt{8} \times \sqrt{2} = \sqrt{8 \times 2} = \sqrt{16} = 4
Marks = 1
1(e) \sqrt{18} \times \sqrt{2}
ANSWER: Multiple Choice (Type 1)
A: \sqrt{20}
B: 36
C: 6
D: \sqrt{24}
Workings: \sqrt{18} \times \sqrt{2} = \sqrt{18 \times 2} = \sqrt{36} = 6
Marks = 1
Question 2:
Write the following surds in the form a√? where a and b are integers.
2(a) \sqrt{20}
ANSWER: Multiple Choice (Type 1)
A: 2\sqrt{10}
B: 2\sqrt{5}
C: 4\sqrt{2}
D: 2\sqrt{3}
Workings: \sqrt{20} = \sqrt{4 \times 5} = \sqrt{4}\sqrt{5}=2\sqrt{5}
Marks = 1
2(b) \sqrt{45}
ANSWER: Multiple Choice (Type 1)
A: 2\sqrt{10}
B: 2\sqrt{3}
C: 4\sqrt{2}
D: 3\sqrt{5}
Workings: \sqrt{45} = \sqrt{9 \times 5} = \sqrt{9}\sqrt{5}=3\sqrt{5}
Marks = 1
2(c) \sqrt{32}
ANSWER: Multiple Choice (Type 1)
A: 16\sqrt{2}
B: 2\sqrt{3}
C: 4\sqrt{2}
D: 3\sqrt{5}
Workings: \sqrt{32} = \sqrt{16 \times 2} = \sqrt{16}\sqrt{2}=4\sqrt{2}
Marks = 1
2(d) \sqrt{24}
ANSWER: Multiple Choice (Type 1)
A: 2\sqrt{6}
B: 3\sqrt{3}
C: 4\sqrt{5}
D: 2\sqrt{7}
Workings: \sqrt{24} = \sqrt{6 \times4} = \sqrt{4}\sqrt{62}=2\sqrt{6}
Marks = 1
2(e) \sqrt{112}
ANSWER: Multiple Choice (Type 1)
A: 2\sqrt{6}
B: 3\sqrt{3}
C: 4\sqrt{5}
D: 2\sqrt{7}
Workings: \sqrt{112} = \sqrt{16 \times7} = \sqrt{16}\sqrt{7}=4\sqrt{7}
Marks = 1
Question 3:
Simplify the following expressions:
Give all answer in its simplest form.
3(a) 3\sqrt{2} \times 3\sqrt{2}
ANSWER: Multiple Choice (Type 1)
A: 18
B: 12
C: 6
D: 8
Workings: 3\sqrt{2} \times 3\sqrt{2} = 9 \times 2 =18
Marks = 1
3(b) \dfrac{\sqrt{50}}{5}
ANSWER: Multiple Choice (Type 1)
A: 5
B: 2
C: \sqrt{2}
D: \sqrt{5}
Workings: \dfrac{\sqrt{50}}{5} = \dfrac{\sqrt{25 \times 2}}{5} = \dfrac{5\sqrt{2}}{5} = \sqrt{2}
Marks = 1
3(c) 2(2\sqrt{2} \times 3\sqrt{2})
ANSWER: Multiple Choice (Type 1)
A: \sqrt{6}
B: 24
C: 32
D: \sqrt{17}
Workings: 2(2\sqrt{2} \times 3\sqrt{2}) = 2(6 \times 2 ) = 24
Marks = 1
3(d) 2\sqrt{2} \times 4 \sqrt{5}
ANSWER: Multiple Choice (Type 1)
A: 5\sqrt{2}
B: 4\sqrt{5}
C: 3\sqrt{6}
D: 8\sqrt{10}
Workings: 2\sqrt{2} \times 4 \sqrt{5} = 8 \times \sqrt{2 \times 5} = 8 \sqrt{10}
Marks = 1
3(e) 4\sqrt{24}- 5\sqrt{6}
ANSWER: Multiple Choice (Type 1)
A: 5\sqrt{2}
B: 4\sqrt{5}
C: 3\sqrt{6}
D: 4\sqrt{7}
Workings: 4\sqrt{24}- 5\sqrt{6} = 4\sqrt{4\times6}- 5\sqrt{6} =8\sqrt{6}-5\sqrt{6}=3\sqrt{6}
Marks = 1
Question 4:
Simplify \sqrt{48}-\sqrt{12}
Giving your answer in the form m\sqrt{3}
ANSWER: Multiple Choice (Type 1)
A: 2\sqrt{3}
B: 4\sqrt{5}
C: 3\sqrt{6}
D: 4\sqrt{12}
Workings: \sqrt{4\times 12}- \sqrt{12} = 2\sqrt{12}- \sqrt{12} =\sqrt{12} = \sqrt{4\times 3} = 2\sqrt{3}
Marks = 3
Question 5:
Expand and simplify the following expressions
5(a) (2-√3)(1+ √3)
ANSWER: Multiple Choice (Type 1)
A: 2\sqrt{3}
B: 4\sqrt{5}
C: \sqrt{3} -1
D: 2+\sqrt{3}
Workings: (2-√3)(1+ √3) = 2 -\sqrt{3}+2\sqrt{3}-3 = \sqrt{3} -1
Marks = 2
5(b) (1-√5)(2+ √3)
ANSWER: Multiple Choice (Type 1)
A: 2-2\sqrt{5}+ \sqrt{3} + \sqrt{15}
B: 2\sqrt{5}+3\sqrt{5} -2
C: 5\sqrt{3} - 2\sqrt{5}
D: \sqrt{3}-\sqrt{7}
Workings: (1-√5)(2+ √3) = 2 -2\sqrt{5} +\sqrt{3} + \sqrt{5 \times 3} = 2-2\sqrt{5}+ \sqrt{3} + \sqrt{15}
Marks = 1
5(c) (2 + 3√4)(6 + 5√3)
ANSWER: Multiple Choice (Type 1)
A: 12 + 24\sqrt{3}
B: 24 + 35\sqrt{6}
C: 12 + 42\sqrt{3}
D: 48 + 40\sqrt{3}
Workings: (2 + 3√4)(6+5\sqrt{3})= 8(6+5\sqrt{3}) = 48 + 40\sqrt{3}
Marks = 2