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Square Root

What Is The Square Root of 25? How To Find The Square Root of 25?

Written by Prerit Jain

Updated on: 17 Aug 2023

What Is The Square Root of 25? How To Find The Square Root of 25?

What Is The Square Root of 25? How To Find The Square Root of 25?

The square root of 25 is 5. The square root of 25 is found using both prime factorization and the long division method. In radical form, the square root is denoted as, and in the exponential form, they are expressed as (25)0.5  and (25)½ The square root of 25 is either 5. The negative value is not used as -5 is not accepted for the rules of finding a square value.

Hence only 5 is considered as the square root of 25. When a number is multiplied by itself it gives the original value as explained or finding the square root of a number is the inversion of squaring the number. 

Finding the square root of 25

  • Prime factorization method
  • Repeated subtraction method
  • Long division method

Prime factorization method

The prime factorization method is one of the simplest methods to find the square root of a number

  • Find the prime factors of 25
    • Prime factor of 25 =  5*5
  • Group the same prime factor
    • By grouping the same prime factor we get 52

No multiplication step is involved as they have only one common factor hence by taking the common prime factor as the result we get 
√25 = 5

Repeated subtraction method 

Repeated subtraction is a handy method for the ones that are not yet familiarized with prime factorization or the long division methods. The numbers that are used for subtraction are the given number and its result with only odd values. Continue the subtraction until zero is obtained. The step in which zero is obtained is the square root of the number. 

  1. 25-1 =24
  2. 24-3 = 21
  3. 21-5 = 16
  4. 16-7 = 9
  5. 9-9 = 0

The number zero is obtained in the 5th step. Hence, √25 = 5

Long division method 

The number that is closest and can divide the dividend is chosen as the divisor.

Hence, √25 = 5

Solved example

Example 1: Using the prime factorization method find the square root of 25.
Prime factor of 25 =  5*5
Hence, √25 = 5

Example 2: Job wants to find the square root of 25 using the long division method, let’s help him.

Hence, √25 = 5

Example 3: The roots of  (25) and -(25) are the same says jack, what did you think?
The negative square has no real root.
25 has real roots while  – (25) has only imaginary roots.
Hence, they are not similar

Example 4: Solve 425 + 325.
√25 = 5
= 4 (5) + 3 (5)
= 20 + 15
= 25

Example 5: What is the value of x, if x25 = 25?
x25 = 25
25 = 5
Hence, x*5 = 25
X = 25/5 = 5
Therefore x = 5

Frequently asked questions

What is the square root of 25?
The 25 = 5.

Is 25 a rational number?
Yes, 25 is a rational number because when we divide the number we get 5 and not 0 (p/q ≠ 0)

What is a perfect square number?
A perfect square number is one when we find the root of the number we get a whole number and not a decimal. 25 = 5 hence 25 is a perfect square number. 

What is the square root of 36?
The square root of 36 is
36 = 6

Ajay bought 25 saplings, and he decided to plant them with the same number in rows and columns, how could he do that?
If Ajay decides to plant equal numbers in both rows and columns then he must have squared them to find how much he should plant for them to be equal.
25 = 5

Therefore, Ajay planted 5 plants in each row and column.

What is the square root of 25?
The square root of 25 = 5.

How to find the square root for irrational numbers?
To find the square root for irrational numbers use the long division method

Written by

Prerit Jain

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