Mental maths · lesson 27 of 28 · free

Estimate divisions and square roots — Mental Maths Mastery

For a quick division, round the divisor to the nearest ten and see which multiple is closest. For a square root, guess the nearest whole number, divide by your guess, and take the average of the two — it lands right next to the true root.

How to do it in your head

Guess, divide, average — “a good guess and a little division get you very close”

  1. Division: round the divisor to the nearest ten and find the closest multiple of it.
  2. Square root: guess the nearest whole root, then divide the number by your guess.
  3. Average the guess and the answer of the division, and round to 1 decimal place.

Use it for: Checking a calculator, Class 8 square roots, and guessing sizes of square plots.

Worked example: √40 to 1 decimal place? → 6.3

  1. 6 × 6 = 36 is the closest square, so guess 6.
  2. 40 ÷ 6 ≈ 6.67.
  3. (6 + 6.67) ÷ 2 ≈ 6.3.

Check: 6.3 × 6.3 = 39.69, very close to 40 ✓

✏️ Practice

Work it out in your head or on paper, type the answer and press Check. Stuck? Press “Show me how”.

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🏁 Lesson 27 test

20 questions. Check each answer, then go to the next one. Get 16 or more right to pass.

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🖨️ Estimating Square Roots and Division Worksheet

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