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.
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
Practice questions for Powers & Roots
What is the value of 2⁻³?
Explain why x⁻¹ = 1/x
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