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Year 7 Maths — Squares and square roots

Square whole numbers and find the square roots of perfect squares.

Name: ________________________

Before you start

Every whole number from zero to twenty-five sits on this line. Find 1, 4, 9, 16 and 25 on it, and look at the gaps between them.

0510152025

The gaps go 3, then 5, then 7, then 9 — the perfect squares spread out as you go, which is why so few numbers have a whole square root.

  1. 1.17² = ?

  2. 2.√576 = ?

  3. 3.A square garden has an area of 169 square metres. How long is each side, in metres?

  4. 4.Work each one out, then put them in order, smallest first.

    • √196
    • √49
    • √144
    • √16
    • √81

  5. 5.Sort each number by whether it is a perfect square.

    Groups: Perfect square · Not a perfect square

    • 70
    • 50
    • 99
    • 64
    • 49
    • 81

  6. 6.What is the smallest whole number, apart from zero, you can multiply 18 by to get a perfect square?

  7. 7.Match each number to its square root.

    • 36
    • 100
    • 121
    • 400
    • 625
    • 6
    • 10
    • 25
    • 11
    • 20

  8. 8.13² = ?

Answer key — Year 7 Maths — Squares and square roots

  1. 1. 289
  2. 2. 24
  3. 3. 13
  4. 4. 1. √16 2. √49 3. √81 4. √144 5. √196
  5. 5. 49 → Perfect square; 64 → Perfect square; 81 → Perfect square; 50 → Not a perfect square; 70 → Not a perfect square; 99 → Not a perfect square
  6. 6. 2
  7. 7. 36 → 6; 100 → 10; 121 → 11; 400 → 20; 625 → 25
  8. 8. 169