Cube roots 1 to 20 are the values that, when multiplied by themselves three times, give the original number. For example, ∛8 = 2 because 2 × 2 × 2 = 8. Among numbers 1 to 20, only 1 and 8 are perfect cubes (∛1 = 1, ∛8 = 2), while the rest have irrational cube root values. This guide provides the complete cube roots 1 to 20 table with decimal values up to 4 places, the cube root formula, methods to calculate cube roots, perfect cubes from 1 to 20, and solved examples for exams.
Cube roots 1 to 20 range from ∛1 = 1 to ∛20 = 2.7144.
Only 1 and 8 are perfect cubes between 1 and 20 (∛1 = 1, ∛8 = 2).
Cube root formula: ∛n = n^(1/3). If x³ = n, then ∛n = x.
∛(a × b) = ∛a × ∛b — cube roots can be split over multiplication.
Cube roots can be negative: ∛(−8) = −2, unlike square roots.
20³ = 8000, while ∛20 = 2.7144 — cubes grow fast, cube roots grow slowly.
Prime factorisation method: group prime factors in threes to find cube roots of perfect cubes.
Common exam values to memorise: ∛2 = 1.26, ∛3 = 1.44, ∛5 = 1.71, ∛10 = 2.15.
Here is the complete table of cube roots from 1 to 20 (values rounded to 4 decimal places):
∛1 = 1.0000 (Perfect cube) ∛2 = 1.2599 ∛3 = 1.4422 ∛4 = 1.5874 ∛5 = 1.7100 ∛6 = 1.8171 ∛7 = 1.9129 ∛8 = 2.0000 (Perfect cube) ∛9 = 2.0801 ∛10 = 2.1544 ∛11 = 2.2240 ∛12 = 2.2894 ∛13 = 2.3513 ∛14 = 2.4101 ∛15 = 2.4662 ∛16 = 2.5198 ∛17 = 2.5713 ∛18 = 2.6207 ∛19 = 2.6684 ∛20 = 2.7144
Key observations: • Only 1 and 8 are perfect cubes in this range • Cube root values increase gradually from 1 to 2.7144 • ∛8 = 2 exactly, because 2³ = 8 • All other values are irrational numbers
A perfect cube is a number that is the cube of a whole number. Among 1 to 20, only two numbers are perfect cubes:
Perfect cubes in 1–20: • 1 = 1³ → ∛1 = 1 • 8 = 2³ → ∛8 = 2
Extended perfect cubes list: • 1 = 1³ → ∛1 = 1 • 8 = 2³ → ∛8 = 2 • 27 = 3³ → ∛27 = 3 • 64 = 4³ → ∛64 = 4 • 125 = 5³ → ∛125 = 5 • 216 = 6³ → ∛216 = 6 • 343 = 7³ → ∛343 = 7 • 512 = 8³ → ∛512 = 8 • 729 = 9³ → ∛729 = 9 • 1000 = 10³ → ∛1000 = 10
How to check if a number is a perfect cube:
This table shows numbers 1 to 20, their cubes, and their cube roots side by side:
Number | Cube (n³) | Cube Root (∛n) 1 | 1 | 1.0000 2 | 8 | 1.2599 3 | 27 | 1.4422 4 | 64 | 1.5874 5 | 125 | 1.7100 6 | 216 | 1.8171 7 | 343 | 1.9129 8 | 512 | 2.0000 9 | 729 | 2.0801 10 | 1000 | 2.1544 11 | 1331 | 2.2240 12 | 1728 | 2.2894 13 | 2197 | 2.3513 14 | 2744 | 2.4101 15 | 3375 | 2.4662 16 | 4096 | 2.5198 17 | 4913 | 2.5713 18 | 5832 | 2.6207 19 | 6859 | 2.6684 20 | 8000 | 2.7144
Notice: While cubes grow rapidly (1 to 8000), cube roots grow slowly (1 to 2.7144).
The cube root of a number n is a value that, when multiplied by itself three times (cubed), gives n.
Symbol: ∛n or n^(1/3)
Definition: If x³ = n, then ∛n = x
Examples: • ∛8 = 2, because 2 × 2 × 2 = 8 • ∛27 = 3, because 3 × 3 × 3 = 27 • ∛1000 = 10, because 10 × 10 × 10 = 1000
Properties of cube roots:
Difference between square root and cube root: • Square root: √n → x² = n (only positive for real numbers) • Cube root: ∛n → x³ = n (can be positive or negative)
There are several methods to find cube roots:
Method 1: Prime Factorisation (for perfect cubes) • Find prime factors and group them in threes • Example: ∛8 = ∛(2 × 2 × 2) = 2 • Example: ∛216 = ∛(2 × 2 × 2 × 3 × 3 × 3) = 2 × 3 = 6
Method 2: Estimation (for non-perfect cubes) • Find the two perfect cubes the number falls between • Example: ∛10 → 2³ = 8 and 3³ = 27, so ∛10 is between 2 and 3 • Since 10 is closer to 8, ∛10 is closer to 2 → ∛10 ≈ 2.154
Method 3: Using the exponent rule • ∛n = n^(1/3) • Use a calculator to compute n^(1/3) • Example: 10^(1/3) = 2.1544
Method 4: Successive approximation • Start with an estimate (say x = 2 for ∛10) • Better estimate = (2x + n/x²) / 3 • Repeat until you reach desired accuracy • For ∛10: x₁ = 2, x₂ = (4 + 10/4)/3 = (4 + 2.5)/3 = 2.167, and so on
For exams, memorising the table is the fastest approach.
Example 1: Find ∛12 + ∛3 Solution: ∛12 = 2.2894, ∛3 = 1.4422 ∛12 + ∛3 = 2.2894 + 1.4422 = 3.7316
Example 2: Simplify ∛16 × ∛4 Solution: ∛16 × ∛4 = ∛(16 × 4) = ∛64 = 4
Example 3: Find the side of a cube with volume 15 cm³ Solution: Side = ∛Volume = ∛15 = 2.4662 cm
Example 4: Evaluate (∛8)² + ∛1 Solution: (∛8)² + ∛1 = 2² + 1 = 4 + 1 = 5
Example 5: A cube has a volume of 5832 cm³. Find its side length. Solution: Side = ∛5832 = ∛(18³) = 18 cm
Example 6: Simplify ∛(8/27) Solution: ∛(8/27) = ∛8 / ∛27 = 2/3
Example 7: Find ∛20 − ∛10 Solution: ∛20 = 2.7144, ∛10 = 2.1544 ∛20 − ∛10 = 2.7144 − 2.1544 = 0.5600
Example 8: If ∛x = 2.5198, find x. Solution: From the table, ∛16 = 2.5198, so x = 16.
Cube roots 1 to 20 are: ∛1 = 1, ∛2 = 1.2599, ∛3 = 1.4422, ∛4 = 1.5874, ∛5 = 1.7100, ∛6 = 1.8171, ∛7 = 1.9129, ∛8 = 2, ∛9 = 2.0801, ∛10 = 2.1544, ∛11 = 2.2240, ∛12 = 2.2894, ∛13 = 2.3513, ∛14 = 2.4101, ∛15 = 2.4662, ∛16 = 2.5198, ∛17 = 2.5713, ∛18 = 2.6207, ∛19 = 2.6684, ∛20 = 2.7144.
Only 1 and 8 are perfect cubes between 1 and 20. 1 = 1³ (so ∛1 = 1) and 8 = 2³ (so ∛8 = 2). The next perfect cube is 27 = 3³, which is beyond 20. All other cube roots in this range are irrational numbers.
The cube root of 8 is 2. This is because 2 × 2 × 2 = 8, or 2³ = 8. Since 8 is a perfect cube, its cube root is a whole number. Using prime factorisation: 8 = 2 × 2 × 2 = 2³, so ∛8 = 2.
There are several methods: (1) Prime factorisation — factorise the number and group in threes. E.g., ∛216 = ∛(6³) = 6. (2) Estimation — find nearby perfect cubes. E.g., ∛10 is between ∛8 = 2 and ∛27 = 3. (3) Exponent method — use n^(1/3) on a calculator. (4) Memorise the table for exams.
A cube is a number multiplied by itself three times: n³ = n × n × n. A cube root is the reverse — finding which number, when cubed, gives the original number: ∛n. Example: The cube of 2 is 2³ = 8. The cube root of 8 is ∛8 = 2. They are inverse operations.
Yes, unlike square roots, cube roots of negative numbers are real and negative. ∛(−8) = −2 because (−2) × (−2) × (−2) = −8. In general, ∛(−n) = −∛n. This is because a negative number multiplied by itself an odd number of times gives a negative result.
∛10 = 2.1544 (rounded to 4 decimal places). Since 2³ = 8 and 3³ = 27, ∛10 lies between 2 and 3 — closer to 2 since 10 is much closer to 8 than to 27. The exact value is irrational and cannot be expressed as a simple fraction.
The cube root symbol is ∛ (a radical sign with a small 3). It is written as ∛n. Alternatively, cube root can be written using exponents as n^(1/3) or n^(0.333...). For example, ∛8 = 8^(1/3) = 2. On calculators, you can use the x^y button with y = 1/3.
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