Square Roots & Cube Roots Exam Pattern Mix

19,600 = 2⁴ × 5² × 7²

Every prime already has an even power

19,600 = 140² is itself a perfect square → divide by 1

Answer: 1

Square both sides: x + 9 = 49

x = 40

Answer: 40

Cube both sides: x/8 = 1.5³ = 3.375

x = 3.375 × 8 = 27

Answer: 27

Formula: (a + b)(a − b) = a² − b²

= 3 − 2 = 1

Answer: 1

√64 = 8

4 decimal places → 2 in the root

√0.0064 = 0.08

Answer: 0.08

Unit digit 1 → root ends in 1 or 9

Drop the last two digits: 146 → 12² = 144 ≤ 146 → tens part 12

Compare with 125² = 15,625: 14,641 is smaller → 121

Answer: 121

(n + 1)² − n² = 2n + 1 = 31

n = 15

The numbers are 15 and 16

Answer: 15 and 16

Let √x = t: t² + t = 72

t² + t − 72 = 0 → (t + 9)(t − 8) = 0

t = 8 → x = 64

Answer: 64

3 3/8 = 27/8

∛27 = 3 and ∛8 = 2

Answer: 3/2

7² = 49

0.07 has 2 decimal places → the square has 4

0.07² = 0.0049

Answer: 0.0049