Work through the levels in order. Type your answer and press Check — open the worked solution if you get stuck. Answers like -6, 3/4 or 0.25 are typed exactly as shown.
Level 1 · Warm-up
1 Solve x2 = 16. (write both, like 4,-4)
Show worked solution
x = ±4, since 4 × 4 = 16 and (−4) × (−4) = 16.
2 Solve x2 = 81. (list them separated by commas)
Show worked solution
x = ±9.
3 How many solutions does x2 = −4 have?
Show worked solution
None. A square is never negative.
Level 2 · Core
4 Solve 3x2 = 27. (list them separated by commas)
Show worked solution
x2 = 9, so x = ±3.
5 Solve 5x2 = 125. (list them separated by commas)
Show worked solution
x2 = 25, so x = ±5.
6 A square has area 100 m2. Side length in metres?
Show worked solution
x = ±10; reject −10 because a length cannot be negative → 10 m.
Level 3 · Challenge
7 Solve 2x2 = 72. (list them separated by commas)
Show worked solution
x2 = 36, so x = ±6.
8 Solve x2 = 45 to 1 decimal place. (positive value only, like 6.7)
Show worked solution
√45 ≈ 6.708, so x ≈ ±6.7 (positive value 6.7).
9 A square garden has area 144 m2. A fence goes all the way round it. How many metres of fence are needed?
Show worked solution
Side: x = ±12, reject −12 → 12 m. Perimeter = 4 × 12 = 48 m.