Mental maths · lesson 18 of 28 · free

Squares up to 30 — Mental Maths Mastery

Split the number into tens and ones. The square is the tens squared, plus two times tens × ones, plus the ones squared — three easy pieces you add in your head.

How to do it in your head

(a + b)² — “a² + 2 × a × b + b²”

  1. Split: 27 = 20 + 7.
  2. Find 20² = 400, 2 × 20 × 7 = 280 and 7² = 49.
  3. Add, biggest first: 400 + 280 + 49.

Use it for: Area of a square, Class 6–8 squares and square roots, and checking (a + b)² in algebra.

Worked example: 27² = 729

  1. 27 = 20 + 7.
  2. 20² = 400, 2 × 20 × 7 = 280, 7² = 49.
  3. 400 + 280 + 49 = 729.

Check: 27 × 27 = 27 × 30 − 27 × 3 = 810 − 81 = 729 ✓

✏️ 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 18 test

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

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🖨️ Squares 1 to 30 Mental Maths Worksheet

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