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Powers & roots practice questions by difficulty

Question bank · Foundation · Grade 1 · Non-calculator

A bank of powers & roots questions to answer on your own. In total: 4 questions (2 warm-up, 1 core, 1 stretch, 1 to 2 marks each), separate from the topic page set. Also here: a multi-part show-that question, 15 quick checks. Before you start, skim the Powers & roots topic page; when stuck, the Powers & roots worked examples.

How to use this page: Aim for two levels right in a row before moving up; open an answer only after you have written yours.

Warm-up questions

2 questions, 1 to 2 marks each. Up first: “What is √25?”

Question 1 Easy1 mark

What is √25?

Show answer

Answer: 5

  1. 5 × 5 = 25.
  2. The square root is 5.
  • Answer (1): Answer 5

Question 2 Easy2 marks

Work out 4³.

Show answer

Answer: 64

  1. 4 × 4 × 4 = 64.
  2. The power is 3.
  • Method (1): 4 × 4 × 4 = 64
  • Accuracy (1): Answer 64

Core questions

1 question, 2 marks each. First up: “Work out 5³.”

Question 3 Medium2 marks

Work out 5³.

Show answer

Answer: 125

  1. 5 × 5 = 25, then 25 × 5 = 125.
  2. The power is 3.
  • Method (1): 5 × 5 = 25, then 25 × 5 = 125
  • Accuracy (1): Answer 125

Stretch questions

1 question, 2 marks each. Starting with: “Work out 10³.”

Question 4 Hard2 marks

Work out 10³.

Show answer

Answer: 1000

  1. 10 × 10 × 10 = 1 000.
  2. The power is 3.
  • Method (1): 10 × 10 × 10 = 1 000
  • Accuracy (1): Answer 1000

Multi-part exam-style question

4 marks over 2 parts. Where the answer is printed, show every line that reaches it. An exam-style question written by Yumio.

Question 5 Exam-style · Show that4 marks

Part (a) is a show that question: the answer is printed and the method earns the marks. Show your working throughout.

(a) What is √100? Show that the answer is 10. [2 marks]

(b) Work out 2⁵. [2 marks]

Show answer and worked solution

Part (a)

Answer: Shown: the working reaches 10

  1. 10 × 10 = 100.
  2. The square root is 10.

Marks for this part:

  • M1: 10 × 10 = 100
  • A1: reaches 10 with every line correct

Part (b)

Answer: 32

  1. 2 × 2 × 2 × 2 × 2 = 32.
  2. The power is 5.

Marks for this part:

  • M1: 2 × 2 × 2 × 2 × 2 = 32
  • A1: Answer 32

Quick checks

Short one-step questions. Pick an option before you open the answer.

Check 1

Work out the value of 1 squared.

  1. 1
  2. 2
  3. 0
Show answer

1 1 × 1 = 1.

Check 2

Work out the value of 2 squared.

  1. 4
  2. 2
  3. 8
Show answer

4 2 × 2 = 4.

Check 3

Work out the value of 3 squared.

  1. 9
  2. 6
  3. 3
Show answer

9 3 × 3 = 9.

Check 4

Work out the value of 11 squared.

  1. 121
  2. 22
  3. 111
Show answer

121 11 × 11 = 121.

Check 5

Work out the positive square root of 4.

  1. 2
  2. 16
  3. 8
Show answer

2 2 × 2 = 4.

Check 6

Work out the positive square root of 9.

  1. 3
  2. 81
  3. 4.5
Show answer

3 3 × 3 = 9.

Check 7

Work out the positive square root of 1.

  1. 1
  2. 0
  3. 2
Show answer

1 1 × 1 = 1.

Check 8

Work out the value of 1 cubed.

  1. 1
  2. 3
  3. 0
Show answer

1 1 × 1 × 1 = 1.

Check 9

Work out the value of 10 to the power 1.

  1. 10
  2. 1
  3. 100
Show answer

10 A power of 1 leaves the number unchanged.

Check 10

Work out the value of 5 squared.

  1. 25
  2. 10
  3. 7
Show answer

25 5 × 5 = 25.

Check 11

Work out the positive square root of 16.

  1. 4
  2. 8
  3. 256
Show answer

4 4 × 4 = 16.

Check 12

Work out the value of 3 cubed.

  1. 27
  2. 9
  3. 6
Show answer

27 3 × 3 × 3 = 27.

Check 13

Is 50 a square number?

  1. No
  2. Yes
  3. Only if you use decimals
Show answer

No 7² = 49 and 8² = 64, so 50 is between two squares.

Check 14

Work out the value of 12 squared.

  1. 144
  2. 24
  3. 121
Show answer

144 12 × 12 = 144.

Check 15

What does the small 3 in 2 cubed count?

  1. How many factors of 2
  2. The number you add
  3. The number you divide by
Show answer

How many factors of 2 A power counts repeated factors.

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