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Square Root

What Is the Square Root of 125? | How to Find the Square Root of 125?

Written by Prerit Jain

Updated on: 12 Aug 2023

What Is the Square Root of 125? | How to Find the Square Root of 125?

What Is the Square Root of 125? | How to Find the Square Root of 125?

The square root of 125 is 11.18 mentioned with a symbol √. The square root of 125 is denoted using 125 is or 1251/2  

The square root of a number is determined when a quantity of a number is produced when multiplied by itself or a factor of a number when multiplied by itself gives the original number. In simple terms when a value is multiplied by itself it gives the original number. For a better understanding. The number 5 when multiplied by itself (5 × 5) = 25. The square root for  (√25) is 5. 

Methods to find the square root of 125

To find the square root of any number first the given number is usually checked to determine whether they are a perfect square number or not. The square of the number s is found using the long division method.

For the number with a perfect square, it is easy to find the square roots and it is a bit tough for non-square values. Numbers like 4,9, 16,25, etc., are perfect squares. Numbers that end with 2,3,7 and 8 are not perfect square numbers.

There are three methods to find the square root of a number

  • Prime factorization method
  • Long division method
  • Repeated subtraction

These methods described above do not apply to finding the square root of any number.  

Prime factorization method

The prime factors of 125 = 5×5×5
125 = 5×√5
= 5× 2.236
Hence, √125= 11.18

Long division method

  • Step 1: Find the smallest integer that can divide the number. 
  • Step 2: Keep following the long division using divisor and dividend. 
  • Step 3: When the particular number of satisfaction is reached the quotient is the square root of the number.  

Find the square root of 125

  • Step 1: Find the smallest integer that can divide the number. 1 is the perfect root number that is smaller and closest to 125.
  • Step 2: Keep following the long division using divisor and dividend. 
Long division method 
Long division method 
  • Step 3: When the particular number of satisfaction is reached the quotient is the square root of the number.

Hence, the √125 = 11.180

Solved examples

Q1: Find the square root of 4 using the prime factorization method
A1: Prime factors of 4 = 2×2
The √4 = 2

Q2: What is the square root of 125?

Long division method

A2: The √125 = 11.180

Q3: What is the square root of 49 using repeated division

  1. 49-1 = 48
  2. 48-3 = 45
  3. 45-5 = 40
  4. 40-7 = 33
  5. 33-9 = 24
  6. 24-11 = 13
  7. 13-13 = 0
    A3: The √49 = 7.

Q4: What is the square root of 3
A4: The square root of 3 = 1.7320

Q5: What is the square root of 5
A5: The √5 = 2.2360

Frequently asked questions

What is the √125?
The √125 = 11.18

Which method is used to find the √125?
The standard method that is used to find the square root of any number is the long division method.

How to write the square root of 125 exponential form? 
1251/2 or 1250.5 is the exponential way to write √125

How to write the square root of 125 in radical form?
The radical form of writing square root is √125

Can I find the square root of 125 using other methods?
Prime factor and the long division are used but the long division method is the most widely used method. 

Is 125 an irrational number?
Yes, 125 is an irrational number since the number is not equal to zero.

What are the methods to find the square root of a number?
There are three methods to find the square root of a number
Prime factorization method
Long division method
Repeated subtraction

We hope that we have answered all your queries regarding the square root of 125!

Written by

Prerit Jain

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