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.
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
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
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.
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.
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
Find the value of:
Evaluate 3\[^{3}\sqrt{8}\] + 7
Solve \[^{3}\sqrt{7}\] - \[^{3}\sqrt{7}\]
Question 1) What is a perfect Cube?
Answer) A perfect cube can be defined as the integer or a whole number as the cube root. Basically, it is where both of the numbers, the cube root, and the value do not have any decimals or fractions. For instance, the cube root 2 and value 8 are whole numbers, we get no decimals or fractions in our final result. Thus, we can safely say that number 8 makes a perfect cube.
Question 2) What is the formula of the Cube Root?
Answer) We use a cube root to give the cube root value of any number. Simply, the cube root formula is denoted by the power of 3 over the number such as n^{3}, where the number represents the number whose cube roots need to be found. E.g. 10^{3} = 1000 (10 × 10 × 10 = 1000).
Question 3) What is the Cube of 1 to 10?
Answer) Here is the cube of 1 to 10
Number | Square | Cube |
1 | 1 | 1 |
2 | 4 | 8 |
3 | 9 | 27 |
4 | 16 | 64 |
5 | 25 | 125 |
6 | 36 | 216 |
7 | 49 | 343 |
8 | 64 | 512 |
9 | 81 | 729 |
10 | 100 | 1000 |
Question 4) Is 400 a perfect Cube?
Answer)The largest integer less than 8 is 7, which has a cube of 343, which is smaller than 400. Technically, however, the smallest number you can add to the number 400 to get a perfect cube is -400, as 0 is the smallest perfect cube (0 x 0 x 0 = 0).