Square Root of 25

The square root of 25 is ±5, where 5 is the positive solution of the equation x² = 25. Finding the square root is just the inverse of squaring a number and hence, squaring 5 will result in 25. 
The square root of 25 is written as √25 in radical form, where the ‘√’  sign is called 
the “radical” sign. In exponential form, it is written as (25)^1/2 .

We can find the square root of 25 through various methods. They are:
i) Prime factorization method
ii) Long division method
iii) Repeated subtraction method

The prime factorization of 25 can be found by dividing the number by prime numbers and continuing to divide the quotients until they can’t be separated anymore, i.e., we first prime factorize 25 and then make pairs of two to get the square root.

So, Prime factorization of 25 = 5 × 5
Square root of 25 = √[5 × 5] = 5

This method is used for obtaining the square root for non-perfect squares, mainly. It usually involves the division of the dividend by the divisor, getting a quotient and a remainder too sometimes.
Follow the steps to calculate the square root of 25:
 Step 1: Write the number 25 and draw a bar above the pair of digits from right to left.
              25 is a 2-digit number, so it is already a pair.
Step 2: Now, find the greatest number whose square is less than or equal to 25. Here, it is 5
              Because 52=25
Step 3: Now divide 25 by 5 (the number we got from Step 2) and we get a remainder of 0.
 
Step 4: The quotient obtained is the square root. In this case, it is 5.
 

We know that the sum of the first n odd numbers is n2. We will use this fact to find square roots through the repeated subtraction method. Furthermore, we just have to subtract consecutive odd numbers from the given number, starting from 1. The square root of the given number will be the count of the number of steps required to obtain 0. Here are the steps:

Step 1: take the number 25 and then subtract the first odd number from it. Here, in this
              case, it is 25-1=24
Step 2: we have to subtract the next odd number from the obtained number until it comes 
             zero as a result. Now take the obtained number (from Step 1), i.e., 24, and again
             subtract the next odd number after 1, which is 3, → 24-3=21. Like this, we have to 
             proceed further.
Step 3: now we have to count the number of subtraction steps it takes to yield 0 finally. 
            Here, in this case, it takes 5 steps 
            So, the square root is equal to the count, i.e., the square root of 25 is ±5.

1)Exponential form
An algebraic expression that includes an exponent. It is a way of expressing the numbers raised to some power of their factors. It includes continuous multiplication involving base and exponent.
Ex: 2 ⤬ 2 ⤬ 2 ⤬ 2 = 16
Or, 2 4 = 16, where 2 is the base, 4 is the exponent.

2)Factorization 
Expressing the given expression as a product of its factors
Ex: 48=2 ⤬ 2 ⤬ 2 ⤬ 2 ⤬ 3

3) Prime Numbers 
Numbers which are greater than 1, having only 2 factors as →1 and Itself. Ex: 1,3,5,7,....

4)  Rational numbers and Irrational numbers

The Number which can be expressed as p/q, where p and q are integers and q not equal to 0 are called Rational numbers. Numbers which cannot be expressed as p/q, where p and q are integers and q not equal to 0 are called Irrational numbers. 

5)  perfect and non-perfect square numbers
Perfect square numbers are those numbers whose square roots do not include decimal places. Ex: 4,9,25 Non-perfect square numbers are those numbers whose square roots comprise decimal places. Ex :3, 8, 24