Estimating square roots without a calculator

2026-11-10Numbers & Estimation Ms Chu

Sandwich a root between consecutive squares to estimate its size.

Key formulas

If a^{2} < N < b^{2} then a < \sqrt{N} < b

What this lesson covers

This lesson builds Secondary 2–3 skill in root estimation. 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 (root estimation) 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 — root estimation

Problem. Apply the method for root estimation with the numbers 6 and 3.

Solution. Identify the rule for root estimation. Substitute 6 and 3 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 root estimation: what is 4+5?

Practice questions

Practice 1 on root estimation: compute with the value 18.
Practice 2 on root estimation: change the numbers and repeat the same method.
Practice 3 on root estimation: write one sentence explaining the key rule.
Practice 4 on root estimation: invent a similar exam-style question and solve it.

Study notes

What is the main idea of root estimation?

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.