The cube root of a number n is the value that, when multiplied by itself three times, gives n. Written as ∛n or n^(1/3). The perfect cube roots in the range 1–50 are: ∛1 = 1, ∛8 = 2, and ∛27 = 3. All other values between 1 and 50 give irrational (non-terminating) decimal cube roots.
Perfect cube roots in 1–50: ∛1=1, ∛8=2, ∛27=3.
∛50 ≈ 3.684 (rounded to 3 decimal places).
All cube roots in 1–50 (except 1, 8, 27) are irrational decimals.
Formula: ∛n = n^(1/3).
∛8 = 2 because 2³ = 2×2×2 = 8.
∛27 = 3 because 3³ = 3×3×3 = 27.
Next perfect cube after 27 is 64 (= 4³), which exceeds 50.
n | ∛n (approx. 3 decimal places) 1 | 1.000 ✓ (perfect cube: 1³=1) 2 | 1.260 3 | 1.442 4 | 1.587 5 | 1.710 6 | 1.817 7 | 1.913 8 | 2.000 ✓ (perfect cube: 2³=8) 9 | 2.080 10 | 2.154 11 | 2.224 12 | 2.289 13 | 2.351 14 | 2.410 15 | 2.466 16 | 2.520 17 | 2.571 18 | 2.621 19 | 2.668 20 | 2.714 21 | 2.759 22 | 2.802 23 | 2.844 24 | 2.884 25 | 2.924
n | ∛n (approx. 3 decimal places) 26 | 2.962 27 | 3.000 ✓ (perfect cube: 3³=27) 28 | 3.037 29 | 3.072 30 | 3.107 31 | 3.141 32 | 3.175 33 | 3.208 34 | 3.240 35 | 3.271 36 | 3.302 37 | 3.332 38 | 3.362 39 | 3.391 40 | 3.420 41 | 3.448 42 | 3.476 43 | 3.503 44 | 3.530 45 | 3.557 46 | 3.583 47 | 3.609 48 | 3.634 49 | 3.659 50 | 3.684
Perfect cubes in 1–50: 1³ = 1 → ∛1 = 1 2³ = 8 → ∛8 = 2 3³ = 27 → ∛27 = 3 (4³ = 64 > 50, so only 3 perfect cubes exist in 1–50)
Perfect cubes to memorise: n | n³ 1 | 1 2 | 8 3 | 27 4 | 64 5 | 125 6 | 216 7 | 343 8 | 512 9 | 729 10 | 1000
How to estimate a cube root: To find ∛35: • 3³ = 27 (too small) and 4³ = 64 (too large) • So ∛35 is between 3 and 4 • 3.2³ = 32.768, 3.3³ = 35.937 • So ∛35 ≈ 3.27 ✓
Cube root formula: ∛n = n^(1/3)
Relation between cube and cube root: • If a³ = b, then ∛b = a • Example: 5³ = 125, so ∛125 = 5
Difference: Cube root vs Square root: • Square root: ∛n → value × itself = n (2nd root) • Cube root: ∛n → value × itself × itself = n (3rd root) • ∛8 = 2 because 2 × 2 × 2 = 8
There are 3 perfect cubes in the range 1–50: ∛1=1 (1³=1), ∛8=2 (2³=8), and ∛27=3 (3³=27). The next perfect cube is 64 (4³), which is beyond 50.
∛50 ≈ 3.684 (rounded to 3 decimal places). Since 3³=27 and 4³=64, ∛50 lies between 3 and 4. More precisely: 3.684³ ≈ 49.97 ≈ 50.
∛27 = 3 exactly, because 3³ = 3×3×3 = 27. This is a perfect cube.
What is a Complete Angle?
Learn the definition of a complete angle (360 degrees). Understand how it relates to acute, obtuse, straight, and reflex angles.
Composite Radicals (Compound Surds) — Definition and Examples
Composite radicals (compound surds) are expressions involving two or more surds. Examples: √2 + √3, √5 − √3. Learn definition, types and rationalisation with FAQs.
Consecutive Even and Odd Numbers in Algebra
Learn how to express consecutive even and consecutive odd numbers in algebra to solve word problems.
Construction of Circumcircle of a Triangle
How to construct the circumcircle of a triangle: draw perpendicular bisectors of two sides, find circumcentre, draw circle. Step-by-step with diagram description. Class 9 10 Maths.
How to Convert Cubic Centimeters ($cm^3$) to Liters (L)
Learn how to convert volume from cubic centimeters (cm3) to liters (L). Discover the conversion formula (divide by 1000) and step-by-step examples.
Turn this guide into revision flashcards, a practice exam, or an AI-generated podcast — free, no signup required.