How to Remember Cube Roots from 1 to 20 Easily
Before we start understanding what is the function of a cube root, let us first understand what exactly a cube root is. Root as we now understand is the lowest number that can be multiplied by itself a certain number of times to get another number. Like in case of square roots we multiply 5 by 5 to get 25 which means the square root of 5 is 25. Similarly, in cube root, we multiply the digit thrice to arrive at an answer. We will elaborate it with an example shortly.
Calculation of Cube Root
How to Find Cube Root of Perfect Cubes?
Let’s calculate the cube root of Let, ‘n’ be the value obtained from \[^{3}\sqrt{216}\], then as per the definition of cubes, n × n × n = n3 = 216. Since 216 is a perfect cube, we will use here the prime factorization method, to get the cube root easily. Here are the following steps for the same.
Prime Factorisation Method
Step 1: Find the Prime factors of 216
216 = 2 × 2 × 2 × 3 × 3 × 3
Step 2: 216 is a perfect cube. Therefore, group the factors of 216 in a pair of three and write in the form of cubes.
216 = (2 × 2 × 2) × (3 × 3 × 3)
216 = 23 × 33
Using the Law of Exponent, we get:
ambm = (ab)m
We get,
216 = 63
Step 3: Now, we will apply the cube root on both the sides
\[^{3}\sqrt{216}\] = \[^{3}\sqrt{6^{3}}\] = 6
Hence, \[^{3}\sqrt{216}\] = 6
How to Find the Cube Root of Non-Perfect Cubes?
We cannot find the cube root of numbers which are not perfect cube using the prime factorization and estimation method. Hence, we will use here some other method.
Let us find the cube root of 30 here. Here, 30 is not a perfect cube.
Step 1: Now we would see 30 lies between 27 ( the cube of 3) and 64 (the cube of 4). So, we will consider the lower number here, i.e. 3.
Step 2: Divide 30 by square of 3 i.e. 30/9 = 3.33
Step 3: Now subtract 3 from 3.33 (whichever is greater) and divide it by 3. So,
3.33 - 3 = 0.33 & 0.33/3 = 0.11
Step 4: At the final step, we have to add the lower number which we got at the first step and the decimal number obtained.
So, 3 +0.11 = 3.11
Therefore, the cube root of 30 is \[^{3}\sqrt{30}\]= 3.11
This is not an accurate value but closer to it.
Let us find the cube root of 1 to 20 natural numbers
Cube Root of 1 to 20
The cube root from 1 to 20 will help students to solve mathematical problems. A list of cubic roots of numbers from 1 to 20 is provided herein a tabular format. The cube root has many applications in Maths, especially in geometry where we find the volume of different solid shapes, measured in cubic units. It will help us to find the dimensions of solids. For example, a cube has volume ‘x’ cubic meter, then we can find the side-length of the cube by evaluating the cube root of its volume, i.e., side = ∛x. Let us see the values of cubic roots of numbers from 1 to 20.
Point to Remember
The square root is when you multiply the lowest digit twice or two times to arrive at the number.
Cube root is when you multiply the lowest number thrice or three times to arrive at the number.
Cube Root List 1 to 100
Questions to be Solved
Example 1: Solve \[^{3}\sqrt{5}\] + \[^{3}\sqrt{7}\].
Solution: From the table, we can get the value of \[^{3}\sqrt{5}\] and \[^{3}\sqrt{7}\]
\[^{3}\sqrt{5}\] = 1.710
\[^{3}\sqrt{7}\] = 1.913
Therefore,
\[^{3}\sqrt{5}\] + \[^{3}\sqrt{7}\] = 1.710 + 1.913
= 3.623
Example 2: Evaluate the value of 4 \[^{3}\sqrt{216}\]
Solution: We know,
\[^{3}\sqrt{216}\] = 6
Therefore,
4\[^{3}\sqrt{216}\] = 4 x 6
= 24
Quiz Time
Find the value of:
Evaluate 3\[^{3}\sqrt{8}\] + 7
Solve \[^{3}\sqrt{7}\] - \[^{3}\sqrt{7}\]
FAQs on Cube Root List 1 to 20: Values, Formulas & Shortcuts
1. What is the list of cubes for numbers 1 to 20?
The cube of a number is that number multiplied by itself three times. Understanding these values helps in quickly identifying perfect cubes. Here is the list of cubes for integers from 1 to 20:
- 1³ = 1
- 2³ = 8
- 3³ = 27
- 4³ = 64
- 5³ = 125
- 6³ = 216
- 7³ = 343
- 8³ = 512
- 9³ = 729
- 10³ = 1000
- 11³ = 1331
- 12³ = 1728
- 13³ = 2197
- 14³ = 2744
- 15³ = 3375
- 16³ = 4096
- 17³ = 4913
- 18³ = 5832
- 19³ = 6859
- 20³ = 8000
2. What is the fundamental difference between a number's cube and its cube root?
The concepts of a cube and a cube root are inverse operations. Cubing a number means multiplying it by itself three times (e.g., the cube of 4 is 4 × 4 × 4 = 64). In contrast, finding the cube root means identifying the number that was originally cubed (e.g., the cube root of 64, or ∛64, is 4). Essentially, one operation builds a number up, while the other breaks it down to its original factor.
3. What makes a number a 'perfect cube'?
A number is called a perfect cube if its cube root is a whole number (an integer with no fractional or decimal part). For example, 125 is a perfect cube because its cube root is 5, which is a whole number. Conversely, 130 is not a perfect cube because its cube root is approximately 5.06, which is not a whole number.
4. Why is learning the cube root list from 1 to 20 important for students?
Memorising the cubes and cube roots from 1 to 20 is highly beneficial for a few key reasons. It dramatically increases calculation speed in exams, especially for topics in algebra and geometry. More importantly, it provides a crucial foundation for estimating the cube roots of larger numbers and for quickly identifying which numbers are perfect cubes, a skill often tested in competitive exams.
5. How can you determine if a number is a perfect cube using prime factorisation?
As per the CBSE syllabus, the prime factorisation method is a reliable way to check for a perfect cube. First, find all the prime factors of the number. If these factors can be grouped into identical triplets (groups of three), the number is a perfect cube. For example, the prime factors of 216 are 2 × 2 × 2 × 3 × 3 × 3. Since these form two triplets, (2×2×2) and (3×3×3), 216 is a perfect cube.
6. Is it possible to find the cube root of a negative number?
Yes, unlike square roots, every real number has a real cube root. The cube root of a negative number will always be negative. This is because multiplying a negative number by itself three times results in a negative product. For example, the cube root of -27 is -3, because (-3) × (-3) × (-3) = -27.
7. What are the common ways to write the cube root of a number?
The cube root of a number, say 'x', has two common mathematical notations. The most frequent is the radical form, written as ∛x. The second is the fractional exponent form, written as x1/3. Both notations represent the same operation: finding a number that, when multiplied by itself three times, equals x.
