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Mathematics for IGCSE & O level - Surds (Section 1)

1
Which of the following is the simplified form of 2√75 - √27?
Answer
(A)
7√3
2
Which of the following is equivalent to 5√3 - √27 ?
Answer
(A)
2√3
3
Which of the following is correct?
Answer
A
C
4
If x = √5+1, find (x-1)^2.
Answer
(B)
5
5
What is the conjugate of 3 - √2?
Answer
(A)
3 + √2
6
When the denominator is of the form a - b√c, to rationalize the denominator, we must multiply the numerator and denominator by:
Answer
(B)
a+b√c
7
If x = 5 + √5 and y = 4 - √5, what is x - y?
Answer
(C)
9
8
What is (√a)^2?
Answer
(B)
a
9
What is the value of (√5 + 1)(√5 - 1)?
Answer
(A)
4
10
Rationalize the denominator of 3/√2.
Answer
(A)
3√2 / 2
11
Which of the following is equivalent to √12?
Answer
(C)
2√3
12
What is the value of √169?
Answer
(A)
13
13
Find the value of x if x = 5 + √5 and x^2 is equal to:
Answer
(A)
30 + 10√5
14
If x=√2+1, what is x^2-2x+1?
Answer
(A)
2
15
Which of the following is a correct way to rationalize the denominator for 1/(√5 - √2)?
Answer
(A)
Multiply by (√5 + √2)/(√5 + √2)
16
Simplify √75 - √48 + √12.
Answer
(B)
3√3
17
Which expression simplifies to a rational number?
Answer
(B)
√9 + √4
18
Simplify √18.
Answer
(A)
3√2
19
If x = 2 and y = √3, what is (x+y)(x-y)?
Answer
(B)
4
20
Simplify (5 + √3) + (2 - √3).
Answer
(A)
7
21
Rationalize the denominator of 4 / (√7 + √3).
Answer
(A)
√7 - √3
22
Simplify √5 - √5/2
Answer
(B)
√5/2
23
Which of the following is not a surd?
Answer
(C)
√16
24
If x = 4+√3, then (x-4)^2 = ?
Answer
(A)
3
25
If (x + √2)(x - √2) = 7, what is the value of x^2?
Answer
(B)
9
26
If a = 2+√3, what is a-2?
Answer
(A)
√3
27
What is the product of the surds: √3 and √12 ?
Answer
(A)
6
28
What is the simplified form of √54?
Answer
(A)
3√6
29
Which expression is equivalent to (√2+√3)^2?
Answer
(A)
5 + 2√6
30
What is the result when you divide √50 by √2?
Answer
(A)
5
31
If x=2+√5, and y=2-√5, what is the value of x*y?
Answer
(A)
-1
32
If x = 2√5 and y = √5, what is x/y?
Answer
(A)
2
33
If x = 3-√2, what is x^2?
Answer
(A)
11 - 6√2
34
If a = √2 and b = √8, find a + b.
Answer
(B)
2√2
35
What is the simplified result of (√3+√2)(√3-√2)?
Answer
(A)
1
36
Simplify: √3 * √6
Answer
(A)
3√2
37
Simplify (5 + √3) - (2 - √3).
Answer
(B)
3 + 2√3
38
If (a+b√c)(a-b√c)=1, then what is the value of a^2-b^2c?
Answer
(A)
1
39
Which statement is TRUE?
Answer
(D)
The product of two surds can be rational.
40
What is the simplest form of the expression √72 ?
Answer
(A)
6√2
41
Rationalize the denominator: 1 / (√3 - 2).
Answer
(C)
-√3 - 2
42
Which of the following is the result when you multiply 3√2 by 2√8?
Answer
(B)
24
43
Which of the following statements are correct?
Answer
A
C
44
What is the result of (3√2) * (√8) ?
Answer
(B)
12
45
Which expression represents the rationalized form of 4/√5?
Answer
(A)
4√5 / 5
46
Simplify √200.
Answer
(A)
10√2
47
The expression 2 + √3 is best described as:
Answer
(D)
An expression of the form a + b√c
48
Simplify (√3 - 1)(√3 + 1)
Answer
(B)
4
49
What is the value of (√5+√7)(√5-√7)?
Answer
(B)
-2
50
If x=√3, what is x^3?
Answer
(A)
3√3