Square Root — O/L Mathematics

How do I practise Square Root?

2 questions with worked solutions

1. Find the square root of 53 to the first decimal place by division or approximation method.
   1. A) 7.5
   2. B) 7.3
   3. C) 7.7
   4. D) 7.1
   Check my answer

   Correct answer: B) 7.3

   Since 7² = 49 and 8² = 64, √53 lies between 7 and 8. Testing 7.3² = 53.29 and 7.2² = 51.84. 53 is closer to 53.29, so √53 ≈ 7.3 to one decimal place.

   Show worked solution

   Step 1: Identify bounding perfect squares: 49 < 53 < 64, so 7 < √53 < 8. Step 2: Linear interpolation approximation: 7 + (53 - 49)/(64 - 49) = 7 + 4/15 ≈ 7 + 0.27 = 7.27. Step 3: Square check: 7.3² = 53.29 (difference +0.29); 7.2² = 51.84 (difference -1.16). Step 4: 53 is much closer to 53.29 than 51.84. Rounding to the first decimal place yields 7.3. Answer: 7.3.
   Modelled on: the O/L Mathematics examination pattern
2. Find the square root of 1296 using prime factorisation.
   1. A) 34
   2. B) 46
   3. C) 38
   4. D) 36
   Check my answer

   Correct answer: D) 36

   As a product of prime factors, 1296 = 2⁴ × 3⁴. Taking a square root halves each index, so √1296 = 2² × 3² = 4 × 9 = 36. Check: 36 × 36 = 1296.

   Show worked solution

   Step 1: Write 1296 as a product of prime factors: 1296 = 2 × 2 × 2 × 2 × 3 × 3 × 3 × 3 = 2⁴ × 3⁴. Step 2: Halve each index: √1296 = 2² × 3². Step 3: Multiply: 4 × 9 = 36. Step 4: Check: 36² = 1296. Answer: 36.
   Modelled on: the O/L Mathematics examination pattern

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Where does Square Root fit in the syllabus?

Grade 10 · Term 1