Square root of 25 – value, derivation and examples

In this article, we will learn about the value and derivation of the square root of 25. The value of root 25 is very easy to find because it is a perfect square. The value of √25 equals 5. The square root of 25 is expressed or represented as √25 in mathematics. The value of root 25 can be positive and negative.  If the root of the square is not a whole number, the final result will be an irrational number. The symbol ‘√’ represents a square root and is also called ‘radical’. 

Perfect and non-perfect squares

• Any number ending with 2, 3, 7, 8 in its unit’s place is not a perfect square. Numbers ending with 1, 4, 5, 6, 9 may be perfect squares.
• 25 is a perfect square of 5, whereas 35 is a non-perfect square

The square root of 25

A value expressed by x = √a represents the square of any natural integer. It means that x is the square root of a. Thus, the square root of any number is equal to a number that gives the original numbers when multiplied by itself. For instance, 5 x 5 = 25, and the square root of the number 25 can be stated to be +5 or -5.

Table of the square root of numbers from 1 to 50

Is root 25 rational or irrational?

If it’s not a perfect square, it’s an irrational number. Because 25 is a perfect square, the number is rational. This means that there will be no decimal places to the square root of 25.

How to find the value of the square root of 25 by prime factorisation?

To find the value of √25 by prime factorisation, follow the steps mentioned below:

1. First, calculate the prime factors of 25 and write them down.
   25 = 5 x 5
2. Group these prime factors in a pair of two factors each.
   25 = 5 x 5
3. Add a square root on both sides.
   √25 = √(5²)
   √25 = (5)^{2 x ½}
   √25 = 5

Solved Question

Question 1: Find the radius of a circle if its area is 25π cm2
Solution – 
Given, the area of the circle = 25π cm²
Now, area = πr² (r is the radius of the circle)
So, 
πr2 = 25π cm²
We get, r2 = 25 cm²
r = √25 cm
 Putting the value of √25 in the above equation, 
We get, r = ±5 cm
Here we will consider the positive value of 5.
Therefore, the radius of the circle is 5 cm.

Question 2: Find the value of ‘x’ if x² = 50
Solution: Given, x² = 50
x = ±√50
x = √(2 x 5 x 5)            (considering that the positive value of root 50)
x = 5√2
we know that √2 = 1.414
so, x = 5 (1.414)
x = 7.07