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Changing subject with powers and roots

2026-12-13Equations & Inequalities Ms Lam

Undo squares and cubes with roots, keeping context signs in mind.

Key formulas

r = \sqrt{A/\pi } for r>0

What this lesson covers

This lesson builds Secondary 2–3 skill in subject with powers. Read the key formulas, study the worked example, then attempt the written practice and the four-question MCQ review.

Method

Write every step. Name the rule you use (subject with powers) before substituting numbers. Keep units and signs visible until the final sentence.

Common mistakes

Students often rush the sign, use the wrong percentage base, or cancel terms instead of factors. Pause after each line and ask whether the step is reversible.

Exam habit

Underline the question verb (simplify, solve, factorise, find). Box the final answer and, where sensible, substitute back for a quick check.

Worked example

Worked example — subject with powers

Problem. Apply the method for subject with powers with the numbers 9 and 4.

Solution. Identify the rule for subject with powers. Substitute 9 and 4 carefully with signs in brackets if needed. Complete each operation on a new line. State the final answer clearly and check by reversing one step.

Review quiz

1 / 4

Warm-up on subject with powers: what is 9+3?

Practice questions

Practice 1 on subject with powers: compute with the value 11.
Practice 2 on subject with powers: change the numbers and repeat the same method.
Practice 3 on subject with powers: write one sentence explaining the key rule.
Practice 4 on subject with powers: invent a similar exam-style question and solve it.

Study notes

What is the main idea of subject with powers?

Apply the stated formula or rule with clear steps, then check by reversing or substituting.

How should I revise this topic?

Cover the worked example, redo the practice without notes, then complete the MCQ set and log any wrong options.