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 13 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 13
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