Cube Root of 15625 by prime factorisation method
CUBE ROOT OF 15625
The cube root of 15625 is equal to 25. It means that the product of 25 thrice by itself gives the number 15625.
Method of finding cube root of 15625
Prime factorisation method
Prime factorization is a method that involves finding the cube root by using its prime factors. The following steps are taken to find the cube root of a number using this method-.
~Select a number whose cube root needs to be found, here we take the number 15625.
~ Divide 15625 with the lowest prime number. Once the number is not divisible by that first selected prime number choose another higher prime number and continue the process until the quotient thus obtained also results in a prime number. The last quotient at the end of the process should result in 1.
| 5 | 15625 |
| 5 | 3125 |
| 5 | 625 |
| 5 | 125 |
| 5 | 25 |
| 5 | 5 |
| 1 |
~ Here we can see that 15625 = 5x5x5x5x5x5
~We can see that when we form a group of 3 numbers, it will result in 53 x 53. On applying the cube root we calculate the product by taking one value from each group and the result is the cube root. Here it will be 25.
In this way, we can find the cube root of any number with the help of the prime factorisation method.
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Frequently Asked Questions
Q1. Is 25 a rational, whole number and integer?
Ans. First of all, we will see whether it is a rational number or not. For rational number, we need to see whether it can be written in the form of p/q with p and q being integers and q≠0, so we can see that 25/1 is written in the form of p/q and q≠0. So, it is a rational number.
We know that the whole numbers include 0 and all natural numbers. Therefore, 25 is a whole number. An integer contains all whole numbers as well as their negatives, so 25 is also an integer.
Q2. How many complex cube roots does 15625 have?
Ans. Every non-zero real number has one real cube root and two complex cube roots. 15625 is a non-zero real number so it also has two complex cube roots.
Q3. What is the nearest perfect cube after 15625?
Ans. 25 is the cube root of 15625. The next perfect cube after 15625 is the cube of 26, which is 17576.