NumberStudy Notes

Worked Example 4: Estimating Roots

Part of Powers & Roots · GCSE GCSE Mathematics revision

This study notes covers Worked Example 4: Estimating Roots within Powers & Roots for GCSE Mathematics. Revise Powers & Roots in Number for GCSE Mathematics with 15 exam-style questions and 22 flashcards. This is a high-frequency topic, so it is worth revising until the explanation feels precise and repeatable. It is section 10 of 14 in this topic. Use this study notes to connect the idea to the wider topic before moving on to questions and flashcards.

Topic position

Section 10 of 14

Practice

15 questions

Recall

22 flashcards

Worked Example 4: Estimating Roots

Estimate √75 to 1 decimal place

Solution

√64 = 8 and √81 = 9

So √75 is between 8 and 9

75 - 64 = 11, 81 - 75 = 6

75 is closer to 81, so closer to 9

Try 8.7: 8.7² = 75.69 ≈ 76

Try 8.6: 8.6² = 73.96 ≈ 74

√75 ≈ 8.7

Keep building this topic

Read this section alongside the surrounding pages in Powers & Roots. That gives you the full topic sequence instead of a single isolated revision point.

Worked Example 3: Negative Bases Higher Level: Fractional and Negative Indices The Power of Powers Understanding Powers and Roots

Practice Questions for Powers & Roots

What is the value of 2⁻³?

A. -8
B. -6
C. ⅛
D. ⅓

1 markfoundation

Explain why x⁻¹ = 1/x

2 markshigher

Quick Recall Flashcards

Cubes: 1³ to 5³

1³ = 1 2³ = 8 3³ = 27 4³ = 64 5³ = 125

Powers of 10

10¹ = 10 10² = 100 10³ = 1,000 10⁴ = 10,000 10⁵ = 100,000 10⁶ = 1,000,000 Pattern: n zeros after 1

15 questions on Powers & Roots — practise free

Instant marking, adaptive difficulty, and 22 spaced repetition flashcards. Free until your GCSEs.

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Worked Example 3: Negative Bases

Higher Level: Fractional and Negative Indices