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  • What is a Cube Root?
    • Mathematical Representation
  • Cube Root Table 1 to 20
  • Cubes of 1 to 20
    • Methods to Find Cube Roots
    • How to Calculate the Values of Cube 1 to 20?
  • Real-Life Applications of Cube Roots
  • Solved Examples cube root of 1 to 20​
  • 1 to 20 cube root FAQs
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Cube Root 1 to 20​
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Cube Root 1 to 20​

By Karan Singh Bisht

|

Updated on 28 Apr 2025, 12:28 IST

In mathematics, the cube root of a number is the value that, when multiplied by itself three times, gives the original number. Cube roots are essential in algebra, geometry, and real-world applications like engineering, physics, and architecture.

For example, the cube root of 8 is 2, because:

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2 × 2 × 2 = 8

In this article, we will cover:

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  • Cube Roots Definition
  • Cube Root Table 1 to 20
  • Cube of 1 to 20
  • Methods to Find Cube Roots
  • Real-Life Applications
  • Solved Examples
  • FAQs

What is a Cube Root?

The cube root of a number x is written as 3√x and represents a value that, when cubed, results in x.

Mathematical Representation

3√x = y if y3 = x

Cube Root 1 to 20​

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For example:

  • 3√27 = 3 because 33 = 27
  • 3√125 = 5 because 53 = 125

Unlike square roots, cube roots can be both positive and negative:

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  • 3√-27 = -3 since (-3) × (-3) × (-3) = -27

Cube Root Table 1 to 20

NumberCube Root (Approx.)
11.000
21.260
31.442
41.587
51.710
61.817
71.913
82.000
92.080
102.154
112.224
122.289
132.351
142.410
152.466
162.520
172.571
182.621
192.668
202.714

Cubes of 1 to 20

NumberCube(n3)
11
28
327
464
5125
6216
7343
8512
9729
101000
111331
121728
132197
142744
153375
164096
174913
185832
196859
208000

Methods to Find Cube Roots

1. Prime Factorization Method

Useful for perfect cubes. Example: Find 3√216.

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  • Prime factors: 216 = 2 × 2 × 2 × 3 × 3 × 3
  • Group into triples: (2×2×2) × (3×3×3)
  • Take one number from each group: 2 × 3 = 6

2. Estimation Method

Useful for non-perfect cubes. Example: Find 3√50.

  • Perfect cubes near 50: 27 and 64
  • Approximate cube root: ~3.7

3. Long Division Method

Useful for precise cube roots but a lengthy process.

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How to Calculate the Values of Cube 1 to 20?

To calculate the cube of numbers from 1 to 20, you simply multiply the number by itself twice. In mathematical terms, cube of a number n is n × n × n.

For example:

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  • Cube of 2 = 2 × 2 × 2 = 8
  • Cube of 5 = 5 × 5 × 5 = 125
  • Cube of 10 = 10 × 10 × 10 = 1000

You can continue this method for all numbers up to 20.

If you want faster results, you can also memorize common cubes or use a scientific calculator to compute them quickly.

Also Check
Associative Property
Centroid of a Triangle
Collinear Points
Commutative Property
Cos 0
Hypotenuse

Real-Life Applications of Cube Roots

  • Engineering and Construction: Calculate dimensions of objects.
  • Physics and Chemistry: Use in fluid dynamics and molecular structures.
  • Computer Science & Data Science: Algorithms involve cube roots for data normalization.
  • Finance and Economics: Compound interest calculations use cube roots.

Solved Examples cube root of 1 to 20​

Q. Evaluate 4 times 10 cube plus 9

Solution: 4 × 103 + 9 = 4 × 1000 + 9 = 4009

Q. Find the value of ∛20-2+(53).

Solution: ∛20 = 2.714

53 = 125

Therefore,

∛20-2+(53) = 2.714 – 2 + 125

= 125.714

Q. Solve 10-∛6.

Solution: ∛6 = 1.817

Therefore,

10-∛6 = 10 – 1.817 = 8.183

Q. Solve ∛3+33.

Solution: ∛3+33

The value of:

∛3 = 1.442

33 = 27

Therefore,

∛3+33 = 1.442 + 27 = 28.442

1 to 20 cube root FAQs

What is the cube root of 1 to 20?

The cube roots of numbers from 1 to 20 are approximate values that tell you what number multiplies by itself three times to give the original number. For example, ∛1 = 1 and ∛8 = 2. The cube roots between 1 and 20 range from 1 to about 2.714.

What is the √ 1 to 20?

The square roots of numbers from 1 to 20 are values that, when squared, give the original number. For example, √4 = 2 and √9 = 3. The square roots start at 1 for 1 and go up to approximately 4.472 for 20.

What are the cubes 1 to 30?

The cubes of numbers from 1 to 30 are the results of multiplying a number by itself twice. For example, 2³ = 8, 3³ = 27, and so on. Some important cubes are:

  • 1³ = 1
  • 5³ = 125
  • 10³ = 1000
  • 20³ = 8000
  • 30³ = 27000

How to solve cube 1 to 20?

To find the cube of numbers from 1 to 20, simply multiply the number by itself twice. For example:

  • Cube of 3 = 3 × 3 × 3 = 27
  • Cube of 7 = 7 × 7 × 7 = 343

What are the perfect cubes from 1 to 20?

Perfect cubes between 1 and 20 are numbers that are cubes of whole numbers. Only two numbers qualify:

  • 1³ = 1
  • 2³ = 8

There are no other perfect cubes under 20.

Is 20 a perfect cube root?

No, 20 is not a perfect cube. A perfect cube has an exact whole number as its cube root, but ∛20 is approximately 2.714, which is not an integer.

How to find the cube root of 197?

To find the cube root of 197, you can:

  • Use a calculator to get ∛197 ≈ 5.817
  • Estimate between nearby perfect cubes (125 and 216) since 197 lies between 5³ and 6³.
  • Apply successive approximation if needed for a closer manual estimate.
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