Square roots of perfect squares

Square roots of perfect squares

Square roots of perfect squares

A perfect square is a whole number you get by multiplying a whole number by itself. So 1, 4, 9, 16, 25, 36 … are perfect squares, because 1 = 1·1, 4 = 2·2, 9 = 3·3, and so on.

Squaring and its opposite

Squaring a number means multiplying it by itself: 7² = 7·7 = 49. The square root does the opposite — it asks "which number, multiplied by itself, gives this?" So √49 = 7, because 7·7 = 49.

Because squaring and taking the square root undo each other, it pays to know the squares up to about 15·15 = 225 by heart. Then √81 = 9 and √144 = 12 come instantly.

A worked example

To find √121, ask: which number times itself is 121? Try 10 → 100 (too small), 11 → 121. So √121 = 11.

Three rules that always help

  • A perfect square is a whole number times itself; its square root is a whole number.
  • The square root undoes squaring, so √(n²) = n.
  • If you know your squares to 15², most grade-8 square roots are instant recall.

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