Square Roots & Cube Roots Diagram-Based Questions

Leaves: 2, 2, 3, 3, 7, 7 → three pairs

Take one from each pair: 2 × 3 × 7

= 42

Trap: 21 drops the pair of 2s.

Answer: 42

Leaves: 3, 3, 3 and 7, 7, 7 → two groups of three

Take one from each group: 3 × 7

= 21

Trap: 63 takes 3 × 3 × 7.

Answer: 21

2450 = 2 × 5² × 7²

Only the 2 has no partner

Multiply by 2: 4900 = 70²

Trap: 5 and 7 are already paired.

Answer: 2

8640 = 2⁶ × 3³ × 5

2⁶ and 3³ are already in groups of three

Remove the lone 5: 8640 ÷ 5 = 1728 = 12³

Trap: 15 also removes a 3 and breaks the 3³ group.

Answer: 5

Side = √2,025 = 45 m

Perimeter = 4 × 45

= 180 m

Trap: 45 is one side only.

Answer: 180

Sides: √576 = 24, √784 = 28, √1,089 = 33

Sum of sides = 85

Fencing = 4 × 85 = 340 m

Trap: 85 adds the sides without multiplying by 4.

Answer: 340

Height² = 13² − 5²

= 169 − 25 = 144

Height = 12 m

Trap: 8 m subtracts the lengths, not their squares.

Answer: 12 m

Along the edges: 30 + 40 = 70 m

Diagonal = √(30² + 40²) = √2,500 = 50 m

Saving = 70 − 50 = 20 m

Trap: 50 is the diagonal, not the saving.

Answer: 20

Upright side = difference in heights = 5 m

Wire = √(12² + 5²) = √169

= 13 m

Trap: 15 m uses the full 9 m height.

Answer: 13 m

Edge = ∛2,744

2,744 ends in 4 → root ends in 4; 2 lies between 1³ and 2³ → 1

Edge = 14 cm

Trap: 52.4 is close to √2,744, a square root.

Answer: 14 cm