Squares, square roots, cubes and cube roots — KCSE Mathematics

KCSE Mathematics · 69 practice questions · 3 syllabus objectives

20 easy17 medium32 hard

What You'll Learn

Key learning outcomes for this topic, aligned to the KNEC KCSE syllabus.

Find squares and square roots of numbers by multiplication, tables and factorisation

Find cubes and cube roots of numbers by multiplication and factorisation

Evaluate expressions involving squares, square roots, cubes and cube roots

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easySHORT ANSWER2 marks

State the cube root of 125. (2 marks)

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Part (a) — 2 marks

Identifies the correct method to find the cube root (1 mk)

Correct answer = 5 (1 mk)

easySHORT ANSWER2 marks

State the value of 12². (2 marks)

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Part (a) — 2 marks

Sets up 12² correctly (1 mk)

Correct answer = 144 (1 mk)

easySHORT ANSWER4 marks

State the value of 7³ and demonstrate how to find ³√{343} using factorisation. (4 marks)

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Part (a) — 2 marks

7³ = 343 (2 mks)

Part (b) — 2 marks

Factorise 343 into its prime factors: 7 × 7 × 7 (1 mk)

State that ³√{343} = 7 (1 mk)

State the value of 5³ and ³√{125}. (4 marks)

Questions match the KCSE syllabus objectives and exam format exactly.

Every answer shows exactly what examiners award marks for.

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