Grade 10 Maths · Algebra

Place a surd between two integers

Find the two whole numbers a square root lies between by using nearby perfect squares (for example √20 is between √16 = 4 and √25 = 5).

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Grade 10 Numbers: Surd between integersMaths Monkey

Grade 10 Algebra Revision: Between which two integers does a squareroot lie?MrsMath

Estimating Surds | Grade 10 MathsAchievEd

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Question 1.2 · March 2025 · Provincial · 2 marks

1.2 Between which two consecutive integers does

170

lie? Show all working details without the use of a calculator.(2)

Work it out on paper first. Then mark yourself with the official memo, one tick at a time.

More past paper questions: place a surd between two integers

Work each one out first, then open the memo and check every tick.

3. Question 1.2 · March 2024 · Provincial · 2 marks
1.2 Write down TWO rational numbers between $2$ and $10$ (Show your working).(2)
Show the memo (2 ticks)Memo
1. ✓
  Identify perfect squares between limitsIntegers between $2$ and $10$ correspond to $4$ and $9$ .
  1 mark · Place a surd between two integers
2. ✓
  State rational numbers $2$ and $3$
  1 mark · Place a surd between two integers
4. Question 1.2 · March 2023 · Provincial · 2 marks
If $x \in {- 2; 2; 4; 5}$ , choose the value of $x$ from the given set that will make the expression $\frac{18}{4 - x}$ be:
1.2 Between which two consecutive natural numbers does $340$ lie. Show all your working out and do so without the use of a calculator.(2)
Show the memo (2 ticks)Memo
1. ✓
  Find perfect cubes $327 < 340 < 364$
  1 mark · Place a surd between two integers
2. ✓
  Determine integers $3 < 340 < 4$
  1 mark · Place a surd between two integers
5. Question 1.2 · March 2022 · Provincial · 2 marks
Four options are provided as possible answers to the following questions. Choose the correct option.
1.2 An irrational number that lies between 5 and 6 is:(2)
1. A $328$
2. B $20 + 8$
3. C $20 \times 8$
4. D $2 π$
Show the memo (1 tick)Memo
1. ✓
  Check values $20 + 8 = 28$ .
  $25 = 5$ and $36 = 6$ .
  $28$ lies between 5 and 6.
  Answer: B
  2 marks · Place a surd between two integers
6. Question 1.4 · March 2022 · Provincial · 2 marks
1.4 Determine two positive integers between which $33$ lies.(2)
Show the memo (2 ticks)Memo
1. ✓
  Identify perfect squares $25 < 33 < 36$
  1 mark · Place a surd between two integers
2. ✓
  State integers5 and 6
  1 mark · Place a surd between two integers

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