Square Roots & Cube Roots Exam Pattern Mix

Both pairs add to 12 under the roots (5 + 7 = 3 + 9).

For a fixed total, roots that are closer together give a larger sum.

√5 + √7 ≈ 2.236 + 2.646 = 4.882

√3 + √9 ≈ 1.732 + 3 = 4.732

Answer: √5 + √7

√x = 7 → x = 49

∛y = 3 → y = 27

x − y = 22

Answer: 22

0.09 + 0.16 = 0.25

? = √0.25 = 0.5

Answer: 0.5

√1.96 = 1.4

√0.0196 = 0.14

1.4 + 0.14 = 1.54

Answer: 1.54

2,700 = 2² × 3³ × 5²

Only 3³ is unpaired → multiply by 3

2,700 × 3 = 8,100 = 90²

Answer: 8,100

∛0.125 = 0.5

∛0.064 = 0.4

0.5 + 0.4 = 0.9

Answer: 0.9

√2601 = 51

√? = 51 − 14 = 37

? = 37² = 1,369

Answer: 1,369

x × √x = 343 → x^(3/2) = 7³

x = (7³)^(2/3) = 7² = 49

Check: 49 × 7 = 343

Answer: 49

x² − 2x = (x − 1)² − 1

x − 1 = √2 → (x − 1)² = 2

2 − 1 = 1

Answer: 1

√0.25 = 0.5

"of" means multiply: 0.5 × 400 = 200

Answer: 200