Cube of 5- Its value and how to find it
When a number is multiplied three times by itself, the answer we get is said to be the cube of that number. In this article, we are going to learn about the cube of 5 and the methods to find the cube of 5.
Value of cube of 5
Meaning
The cube of a number is said to be the number multiplied three times by itself. For example the cube of 4 is 64( as 4 x 4 x 4 =64). The exponential form of the cube of a number is x3 where x is any number.
Method of finding cube of a number
Method 1
~Number ending with zero-:
Firstly, we will find the cube of the number formed by the non-zero digits of the given number. Then, we will multiply that cube by 1000.
For example-
Cube of 50 = 53 x 1000
= 125 x 1000
= 125000
~ In the case of 5 it is multiplied three times by itself to obtain the cube, i.e, the cube of 5= 5×5×5 =125
Method 2
Under this method, we find a cube of a number by using two algebraic formulas-:
(p + q)3 = p3 + q3 + 3pq(p + q) or (p – q)3 = p3 – q3 – 3pq(p – q)
We can write 53 as (3 + 2)3
On applying the first expression, we get
(3 + 2)3 = 33 + 23 + 3×3×2(3 + 2)
= 27 + 8 + 18×5
= 27 + 8 + 90
= 125
We can write 53 as (6 – 1)3
On applying the second expression
(6 – 1)3= 63 – 13 – 3×6×1(6 – 1)
= 216 – 1 – 18×5
= 125
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Frequently Asked Questions
Q1. Is it possible that the cube of an odd number is an even number?
Ans No, it is not possible that the cube of an odd number is an even number. It must be noted that the cube of an odd number will be an odd number and the cube of an even number will be an even number.
Q2. What is the cube of negative 5?
Ans The cube of -5 = -5×-5×-5
= (-5)3
= -125.
Hence, the cube of negative 5 is equal to negative 125.
Q3. Is 5 a rational number?
Ans. Yes, 5 is a rational number as it can be written in the form of p/q with p and q being integers and q is not equal to 0.