√8 simplifies to 2√2 and √50 simplifies to 5√2, so this Year 11 sheet opens by pulling square factors out of surds for the chapter. The answers then record 3 as a simplified result and √2 ÷ 2 as a rationalised fraction's denominator.
Key Takeaways
√8 = 2√2 (Q1).
√50 = 5√2 (Q2).
Q4 records √2 ÷ 2 as a rationalisation answer.
Section A: Multiple Choice Questions (1 Mark Each)
Choose the correct option for each question.
1.Simplify √8.
(a) 4√2(b) 2√2(c) √4(d) 2√4
2.Simplify √50.
(a) 2√5(b) 10√2(c) 5√2(d) √25
3.The value of √3 × √3 is what?
(a) √6(b) 3(c) 9(d) √9
4.Rationalise the denominator of 1 ÷ √2.
(a) √2 ÷ 2(b) 2(c) √2(d) 2 ÷ √2
5.Simplify √12.
(a) 6√2(b) 2√6(c) 3√2(d) 2√3
6.Expand (3 + √5)(3 - √5).
(a) 9(b) 14(c) 4(d) 9 - 2√5
Section B: Short Answer Type Questions (2 Marks Each)
Show all steps clearly.
7.Simplify √27.
8.Simplify √45.
9.Rationalise the denominator of 1 ÷ √5.
10.Simplify (√5)².
11.Write 2√18 in the form a√2.
12.Simplify √2 × √8.
13.Expand and simplify √3(√3 + 2).
14.Simplify √72.
Section C: Numericals & Word Problems (3 Marks Each)
Apply the concepts to solve the problems. Show all working.
15.A square has area 32 cm². Give its side length in the form a√2.
16.A rectangle has length √18 cm and width √2 cm. Find its area.
17.A right-angled triangle has legs of length √5 cm and √20 cm. Find the length of the hypotenuse.
18.Simplify √75 + √27 as a single surd term.
19.Rationalise the denominator of 4 ÷ √3 and leave your answer in simplest surd form.
20.A rectangle has area √6 cm² and width √3 cm. Find its length in surd form.
Answer Key
1. b) 2√2
2. c) 5√2
3. b) 3
4. a) √2 ÷ 2
5. d) 2√3
6. c) 4
7. Refer to solution guide.
8. Refer to solution guide.
9. Refer to solution guide.
10. Refer to solution guide.
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14. Refer to solution guide.
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17. Refer to solution guide.
18. Refer to solution guide.
19. Refer to solution guide.
20. Refer to solution guide.
End of Worksheet
People Also Ask
What is √8 simplified?
2√2, option (b) in this worksheet (Q1).
What is √50 simplified?
5√2, option (c) in this worksheet (Q2).
What is √12 simplified?
2√3, option (d) in this worksheet (Q5).
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