1
Find the perfect squares either side
2
Example: √50 is between √49 = 7 and √64 = 8
3
50 is closer to 49 than 64, so √50 ≈ 7.1
4
Check: 7.1² = 50.41 ✓
This deep dive covers Method: Estimating Square 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 5 of 14 in this topic. Use this deep dive to connect the idea to the wider topic before moving on to questions and flashcards.
Practice questions for Powers & Roots
What is the value of 2⁻³?
Explain why x⁻¹ = 1/x
Quick recall flashcards
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
Cubes: 1³ to 5³
1³ = 1
2³ = 8
3³ = 27
4³ = 64
5³ = 125