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The cube of a number (x) is the resultant number when it is multiplied three times. Then , the cube of the number (x) is x3 or x-cubed. Let’s use the number 5 as an example. We already know 5 × 5 × 5 = 125 As a result, 125 is known as the 5 cube. The cube root of a number, on the other hand, is the inverse of the cube of a number and is written by ∛ In the same way, 5 is known as the cube root of the No. 125. On this page, we’ll study more about a number’s cubes and cube roots.
Cube of a number
The final number multiplying a number three times by itself is known as the cube of the original number. It’s called a cube since it’s used to show the volume of a cube. In other terms, the cube of a number increased to exponent 3 is termed the number.
Formula for Cube Roots
The cube root formula is used to find the cube root of any number stated in radical form with the sign ∛ It can be determined using the cube root formula after first determining the prime factorization of the given number. Assume that x is any number that x = y × y × y.
where, Any number x has a cube root of y.
This also implies that if y has an integer value, the number x is a perfect cube.
How to find cube root of big numbers
To find the cube root of a number, apply the prime factorization method. To find the cube root, start by determining the number’s prime factorization. Then, divide the components into three groups of three elements each. After that, erase the cube root symbol and multiply the factors to get the answer. The specified number is not a perfect cube, and the cube root of that integer cannot be computed if any factor remains that cannot be divided evenly into groups of 3.
How to calculate cube root quickly
The cube root can be quickly found using the prime factorization method.
The prime factorization method can be used to find the cube root of any perfect cube. This procedure is comparable to determining the square root. Finding the cube root entails the following steps:
- The given number’s prime factors are written down.
- Shares is a notation for writing prime factors of similar numbers.
- From each trio, one factor is picked.
- The cube root of a given number is the product of chosen factors.
Example 1: 38
Prime factorization of 8 = 2 x 2 x 2.
Then ∛ (2 x 2 x 2) = ∛23 = 2.
Example 2: ∛3375
Prime factorization of 3375 = 3 x 3 x 3 x 5 x 5 x 5.
So, ∛ (3 x 3 x 3 x 5 x 5 x 5) = ∛33 x 53 = ∛153 = 15
Cube Root Formula’s Applications
A few important applications of the cube root formula are listed below.
- Cubic equations to be solved
- If the volume of a cube is known, calculate its dimensions.
- Give a more precise apartment measurement
Conclusion
In this article we learn about the cube root of numbers and its formulas , applications . When solving cubic equations, the cube root is frequently utilized. It can be used to find the dimensions of a three-dimensional object of a given volume, for example. In real life, cube roots are used to find the edge of a cube with a particular volume. The height of a satellite was calculated using cube roots. As it orbits the planet in the direction of the Earth’s rotation, it stays above the same equatorial spot on the planet’s surface. cube roots is a notion.
