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Mathematics for IGCSE & O level - Surds (Section 2)

1
What is the result of √4 + √16?
Answer
(A)
6
2
If a = √3-√2, then a^2 = ?
Answer
(A)
5-2√6
3
Which of the following is equivalent to √72 - √8?
Answer
(B)
2√2
4
Which of the following is not equal to 2√3?
Answer
(D)
√24
5
What is the value of a^2 - b^2 if a= √5 and b= √2?
Answer
(A)
3
6
If x = 2√3 and y = 3√2, what is xy?
Answer
(A)
6√6
7
If x = 5 + √5 and y = 4 - √5, what is x + y?
Answer
(A)
9
8
Simplify (√5 + 2)(√5 - 2).
Answer
(C)
-1
9
Which of the following is a simplified form of √27 + √12?
Answer
(A)
5√3
10
Which of the following expressions results in a rational number?
Answer
A
C
11
What is the result of (√3 + √2)^2 ?
Answer
(B)
5 + 2√6
12
If x = 1 + √2, and y = 1 - √2. What is x+y?
Answer
(B)
2√2
13
Which of the following is a surd?
Answer
(C)
√2
14
Rationalize the denominator of (√2) / (2-√2)
Answer
(A)
(2√2+2)/2
15
What expression is obtained when rationalizing the denominator of (2+√3)/(2-√3) ?
Answer
(A)
7+4√3
16
Which of the following is true regarding surds?
Answer
A
B
D
17
Rationalize the denominator of 5 / (2√3).
Answer
(A)
5√3/6
18
What is the simplified form of √98 / √2?
Answer
(B)
7
19
What is the simplest form of 3√18 + 2√8?
Answer
(A)
13√2
20
If x = √6 - √5, what is the value of x^2 + 2√30?
Answer
(B)
11
21
Which of these are in the form a + b√c?
Answer
B
C
22
Simplify √18.
Answer
(A)
3√2
23
Simplify (5 + √3)(2 - √3).
Answer
(A)
7 - 3√3
24
If x = 4 + √7, what is x^2 - 8x + 9?
Answer
(B)
23
25
Rationalise the denominator of 2/ (3-√5)
Answer
(A)
(6+2√5) / 4
26
Simplify √50 - √8.
Answer
(A)
3√2
27
Find the value of a such that (2 + √3)(a - √3) is rational.
Answer
(A)
2
28
Which of the following results in a rational number?
Answer
A
B
29
If x = 2 + √3, then (x-2)^2 is equal to:
Answer
(A)
3
30
Which expression is equal to 3 - 4√2?
Answer
(A)
(1-√2) - (2-3√2)
31
Rationalize the denominator of 5 / (√7 - √2).
Answer
(B)
√7 + √2
32
Which of the following is equivalent to (√3 - √2)^2?
Answer
(A)
5 - 2√6
33
Which of the following is the simplest form of √108?
Answer
(A)
6√3
34
Simplify √27 - √12.
Answer
(A)
√3
35
Which of the following is a rational number?
Answer
(C)
√9
36
Which of the following results in a rational number?
Answer
A
B
D
37
Simplify (√5 + 2) / (√5).
Answer
(A)
1 + (2√5)/5
38
Simplify √98.
Answer
(A)
7√2
39
What is the result of rationalizing the denominator of 4/(2√3)?
Answer
(A)
2√3 / 3
40
Given x=√3+1 and y=√3-1, what is xy?
Answer
(B)
2
41
Which of the following is the simplified form of √(8) + √(32) - √(2)?
Answer
(B)
5√2
42
Which of the following is equivalent to 5√2 + 2√8 - √18?
Answer
(A)
6√2
43
Rationalize the denominator of 6 / (2 - √3).
Answer
(A)
12 + 6√3
44
Which of the following is the simplified form of (√6) * (√10) / √15?
Answer
(B)
2√2
45
What is the value of x if x + y = 6 + 3√3 and y = 2 - √3?
Answer
(A)
4+2√3
46
Given x = 3 - √2, what is the value of x^2?
Answer
(A)
11 - 6√2
47
Which of the following is the simplified form of √(12) - √(75) + √(3)?
Answer
(B)
-4√3
48
Which of the following options can be written as a + b√c, where a, b, and c are integers?
Answer
A
B
C
49
Rationalize the denominator: 1/ (√5 + 2).
Answer
(B)
2-√5
50
What is the simplified form of (2 / √3) - √3 ?
Answer
(B)
-√3 / 3