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The square of a number is the number times itself: 42² = 42 × 42 = 1764, and the square root goes back: √1764 = 42. A perfect square has all its prime factors in pairs, so 72 = 2 × 2 × 2 × 3 × 3 needs one more 2 to become a perfect square (144). The sum of the first n odd numbers is always n².
✓ You passed this lesson’s test.
Pairs make squares — “a perfect square has every prime factor in pairs”
Use it for: Square gardens and tiles, Pythagoras, arranging chairs in equal rows and columns, and the squares and square roots chapter of Class 8 maths.
Check: 42² = 1600 + 2 × 40 × 2 + 4 = 1600 + 160 + 4 = 1764 ✓
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20 sums. Check each answer, then go to the next one. Get 16 or more right to pass.
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