Surds (Copy)
Practice Questions — 1.18 Surds
Question 1
Simplify √20.
Question 2
Simplify √72.
Question 3
Simplify √50 − √18.
Question 4
Simplify √200 − √32.
Question 5
Simplify √245.
Written and Compiled By Sir Hunain Zia, World Record Holder With 154 Total A Grades, 7 Distinctions and 11 World Records For Educate A Change O Level And IGCSE Mathematics Full Scale Course
Question 6
Simplify √12 + √75.
Question 7
Simplify √8 × √2.
Question 8
Simplify √45 ÷ √5.
Question 9
Simplify √3 × √27.
Question 10
Simplify (√18)².
Written and Compiled By Sir Hunain Zia, World Record Holder With 154 Total A Grades, 7 Distinctions and 11 World Records For Educate A Change O Level And IGCSE Mathematics Full Scale Course
Question 11
Rationalise the denominator: 5 / √10.
Question 12
Rationalise the denominator: 3 / √12.
Question 13
Rationalise the denominator: 7 / √5.
Question 14
Rationalise the denominator: 2 / √3.
Question 15
Rationalise the denominator: (√2) / (√8).
Written and Compiled By Sir Hunain Zia, World Record Holder With 154 Total A Grades, 7 Distinctions and 11 World Records For Educate A Change O Level And IGCSE Mathematics Full Scale Course
Question 16
Simplify (2√5)(3√2).
Question 17
Simplify (√7)(√28).
Question 18
Simplify √18 + √50 − √8.
Question 19
Simplify (√3 + √2)(√3 − √2).
Question 20
Simplify (2 + √5)(2 − √5).
Written and Compiled By Sir Hunain Zia, World Record Holder With 154 Total A Grades, 7 Distinctions and 11 World Records For Educate A Change O Level And IGCSE Mathematics Full Scale Course
Question 21
Simplify (√6 + √3)².
Question 22
Simplify (√5 − 2)².
Question 23
Simplify (√2 + 3)(√2 − 3).
Question 24
Simplify (√3 + √7)².
Question 25
Simplify (2√2 − √3)².
Written and Compiled By Sir Hunain Zia, World Record Holder With 154 Total A Grades, 7 Distinctions and 11 World Records For Educate A Change O Level And IGCSE Mathematics Full Scale Course
Question 26
Simplify (√2/3) × (√18/5).
Question 27
Simplify (√12/7) ÷ (√3/14).
Question 28
Simplify (√50 − √2)(√50 + √2).
Question 29
Simplify (3√2 + 2√3)(3√2 − 2√3).
Question 30
Simplify (√11 + √5)(√11 − √5).
Written and Compiled By Sir Hunain Zia, World Record Holder With 154 Total A Grades, 7 Distinctions and 11 World Records For Educate A Change O Level And IGCSE Mathematics Full Scale Course
Answer key and explanations — 1.18 Surds
1.
√20 = √(4 × 5) = 2√5
Explanation: Factor 20 into a square × other factor.
2.
√72 = √(36 × 2) = 6√2
3.
√50 − √18 = (5√2) − (3√2) = 2√2
4.
√200 − √32 = (10√2) − (4√2) = 6√2
5.
√245 = √(49 × 5) = 7√5
Written and Compiled By Sir Hunain Zia, World Record Holder With 154 Total A Grades, 7 Distinctions and 11 World Records For Educate A Change O Level And IGCSE Mathematics Full Scale Course
6.
√12 + √75 = (2√3) + (5√3) = 7√3
7.
√8 × √2 = √16 = 4
8.
√45 ÷ √5 = √(45 ÷ 5) = √9 = 3
9.
√3 × √27 = √81 = 9
10.
(√18)² = 18
Written and Compiled By Sir Hunain Zia, World Record Holder With 154 Total A Grades, 7 Distinctions and 11 World Records For Educate A Change O Level And IGCSE Mathematics Full Scale Course
11.
5 / √10 × √10/√10 = 5√10 / 10 = √10 / 2
12.
3 / √12 = 3 / (2√3) × √3/√3 = 3√3 / 6 = √3 / 2
13.
7 / √5 × √5/√5 = 7√5 / 5
14.
2 / √3 × √3/√3 = 2√3 / 3
15.
(√2 / √8) = √(2/8) = √(1/4) = 1/2
Written and Compiled By Sir Hunain Zia, World Record Holder With 154 Total A Grades, 7 Distinctions and 11 World Records For Educate A Change O Level And IGCSE Mathematics Full Scale Course
16.
(2√5)(3√2) = 6√10
17.
(√7)(√28) = √196 = 14
18.
√18 + √50 − √8 = (3√2) + (5√2) − (2√2) = 6√2
19.
(√3 + √2)(√3 − √2) = (√3)² − (√2)² = 3 − 2 = 1
20.
(2 + √5)(2 − √5) = 4 − 5 = −1
Written and Compiled By Sir Hunain Zia, World Record Holder With 154 Total A Grades, 7 Distinctions and 11 World Records For Educate A Change O Level And IGCSE Mathematics Full Scale Course
21.
(√6 + √3)² = (√6)² + 2(√6)(√3) + (√3)² = 6 + 2√18 + 3 = 9 + 6√2
22.
(√5 − 2)² = (√5)² − 2×2√5 + 2² = 5 − 4√5 + 4 = 9 − 4√5
23.
(√2 + 3)(√2 − 3) = (√2)² − 9 = 2 − 9 = −7
24.
(√3 + √7)² = (√3)² + 2√21 + (√7)² = 3 + 2√21 + 7 = 10 + 2√21
25.
(2√2 − √3)² = (2√2)² − 2(2√2)(√3) + (√3)² = 8 − 4√6 + 3 = 11 − 4√6
Written and Compiled By Sir Hunain Zia, World Record Holder With 154 Total A Grades, 7 Distinctions and 11 World Records For Educate A Change O Level And IGCSE Mathematics Full Scale Course
26.
(√2/3) × (√18/5) = √36 / 15 = 6/15 = 2/5
27.
(√12/7) ÷ (√3/14) = (√12/7) × (14/√3) = (14√12)/(7√3) = 2√(12/3) = 2√4 = 4
28.
(√50 − √2)(√50 + √2) = (√50)² − (√2)² = 50 − 2 = 48
29.
(3√2 + 2√3)(3√2 − 2√3) = (3√2)² − (2√3)² = 18 − 12 = 6
30.
(√11 + √5)(√11 − √5) = 11 − 5 = 6
Written and Compiled By Sir Hunain Zia, World Record Holder With 154 Total A Grades, 7 Distinctions and 11 World Records For Educate A Change O Level And IGCSE Mathematics Full Scale Course