Numbers and operations · Ages 13–14

Working with surds worksheet

Part of: Surds & irrational numbers

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Numbers and operations · Ages 13–14

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Write each answer in the space. For word problems, show your working and write a sentence answer.

13.Someone works out 9 + 16 and gets 5. What is wrong? What is the right answer?
1. (1)9 + 16 = 9 + 16
2. (2)= 25
3. (3)= 5
Find the wrong step, then write the right answer
Working:
Answer:
14.A square has sides of 28 cm. In simplest surd form its perimeter is cm.
Fill in each blank
Working:
Answer:
15.Tsz-ching says 66 × 46 = 24. Tsz-ching is right.
True or false?
Working:
Answer:
16.Rationalise the denominator of 546. Put the steps in order.
- A. 546 = (54 × 6) ÷ (6 × 6)
- B. 546 ÷ 6 = 96
- C. (54 × 6) ÷ (6 × 6) = 546 ÷ 6
Write the letters in the right order
Working:
Answer:
17.A rectangle is 57 cm long and 77 cm wide. Its perimeter is cm and its area cm².
Fill in each blank
Working:
Answer:
18.A rectangle has an area of 90 cm² and is 63 cm long. How wide is it?
- A. 153 cm
- B. 5 cm
- C. 53 cm
- D. 15 cm
Choose the right answer
Working:
Answer:

Show the answers and working

Working with surds worksheet: Answers and working

1. 6, 11
Like surds subtract: (12 − 6)11 = 611.
2. 7, 2
Like surds combine like 2x + 5x: (2 + 5)2 = 72.
3. 10, 3
Like surds combine like 6x + 4x: (6 + 4)3 = 103.
4. 5
Multiply top and bottom by 7: 357 ÷ 7 = 57.
5. 9, 3
Simplify first: 75 = 53 and 48 = 43; like surds add to 93.
6. 30, 14
Outside times outside, inside times inside: (5 × 2)6 × 21, and 6 × 21 = 314, so 3014.
7. 2
Multiply top and bottom by 2: 42 ÷ 2 = 22.
8. 25
(x + y)(x − y) = x² − y²: (29)² − 2² = 29 − 2² = 25; the root is gone.
9. 1, 2
18 = 32 and 32 = 42; 3 × 3 − 2 × 4 = 1, so 12.
10. 16, 8, 3
(x + y)² = x² + 2xy + y²: 12 + 4 + 248 = 16 + 83.

Marking: 2 for the working, 1 for the answer, 1 for the sentence.

13. 7
a + b isn't a + b: take each root, 9 = 3 and 16 = 4, so the sum is 3 + 4 = 7.
14. 8, 7
28 = 27, so the perimeter is 4 × 27 = 87 cm.
15. False
6 × 6 = 6, so 66 × 46 = 6 × 4 × 6.
16. A → C → B
Multiply top and bottom by 6, making the bottom 6; then cancel, 54 ÷ 6 = 9.
17. 24, 7, 245
Perimeter = 2 × (57 + 77) = 247; area = 57 × 77 = 5 × 7 × 7 = 245.
18. C. 53 cm
Width = 90 ÷ (63) = 153 = 153 ÷ 3 = 53 cm.

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