Square root of 104
2026-02-28 08:35 Diff
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Last updated on August 5, 2025

A square root is a number when multiplied by itself gives the original number. The square of a number is represented as X² and the square root of a number is expressed as √x The square root of 104 is represented by √104 Square roots play a vital role in physics to determine the velocity of an object in free fall.

What Is the Square Root of 104?

The square root of 97 is approximately ±10.198


The square root of 104 is written as √104 in radical form. In exponential form, it is written as (104)1/2
 

Finding the Square Root of 104

We can find the square root of 104 through various methods. They are:


i) Prime factorization method


ii) Long division method


iii) Approximation/Estimation method
 

Square Root of 104 By Prime Factorization Method

To find the square root of 104 through the Prime Factorization method, there are various steps involved in the process:


Step 1: To find the square root of 104, first express it in its prime factors. 


Here, 104 = 2×2×2×13 


Step 2: Simplify the factors further 


104 = 23 × 13

Step 3: Apply root on both sides


√104 = √(2×13)


√104 = 2√26 


2√26 = 10.198

Therefore, the square root of √104 = 10.198
 

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Square Root of 104 By Long division

Finding a square root of 104 by long division method consists of the following steps:


Step 1: Pair the digits by putting a bar above. Starting from the right, we will pair 04 and 1 separately. We will also pair the zeros in decimals in pairs of 2 from left to right.


Step 2: Find a number, when multiplied by itself, gives a product less than or equal to 1. Here it's 1, so place 1 in the quotient and the divisor place will result in the remainder 0.


Step 3: Bring down 4 beside the remainder 0, add the divisor to itself and write it below. 1+1=2  


Step 4: Find the remainder and bring down the pair of 0s from the decimal part of the number. Adding X to the divisor, the new divisor remains 20. 


Step 5: Repeat the process to get the decimal places you want 


Therefore, the √104 = 10.198 
 

Square Root of 104 By Approximation

Steps to find the square root of 104 by approximation method are:


Step 1: First identify the perfect squares around 104. 


We know that 


102 = 100


112 = 121


So √104 is between 10 and 11. 


Step 2: Since 104 is closer to 100 than 121, we can start by estimating a bit above 10. Let us go with 10.2
10.2×10.2 = 104.04, which is close to 104.  

Step 3: To get a more precise value, we can continue with more decimal places
10.192 = 103.8361, it is slightly less than 104. 

Step 4: Try 10.20


10.202 = 104.04, which is very close to 104. 


Thus, the √104 is approximately 10.198
 

Common Mistakes and How to Avoid Them in the Square Root of 104

While finding the square root of 104, we often make some common mistakes, especially when we solve problems related to that. So, let’s see some common mistakes and their solutions
 

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Problem 1

Jimmy wants to calculate the side length of the square loan at his home. It has an area of 104 square feet.

Okay, lets begin

√104 = 10.198


Hence the length of the loan is approx 10.198


Ans: 10.198
 

Explanation

To find the side length of the loan, we need to find the √104
 

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Problem 2

What will be the distance covered by a train travelling at √104 miles per hour in 12 hours?

Okay, lets begin

Distance covered = Speed x Time


√104×2 = 10.198×12 = 122.376 miles


Ans: 122.376 miles
 

Explanation

Apply the distance formula. Find the √104 and multiply it by 12 to get the desired distance. 
 

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Problem 3

Why is the square root of 104, not a whole number?

Okay, lets begin

The square root of 104 is not a whole number because 104 is not a perfect square. A perfect square is a number that can be expressed as the product of two equal whole numbers.


Hence, √104 is not a whole number. 
 

Explanation

For example, 25 is a perfect square because 5 × 5 = 25. However, 104 cannot be expressed as the product of two equal whole numbers, so its square root is not a whole number.
 

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Problem 4

How can we find the exact value of the square root of 104?

Okay, lets begin

The exact value of the square root of 104 cannot be expressed as a simple fraction or decimal. It is an irrational number.


We cannot find the exact value of √104
 

Explanation

Irrational numbers are numbers that cannot be expressed as a simple fraction. The square root of 104 is one such number.

While we can approximate its value using methods like estimation or calculators, there is no exact, finite decimal representation.
 

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Problem 5

Can we find the square root of 104 using a calculator?

Okay, lets begin

Yes, we can find the square root of 104 using a calculator. Most calculators have a square root function.

Explanation

 Enter 104 into the calculator and then press the square root button. The calculator will display the approximate value of the square root.

Well explained 👍

FAQs on 53 Square Root

1.How do you simplify √104

 We can simplify by factorizing 104 and finding the square root.

2.What are the factors of 104?

1, 2, 4, 8, 13, 26, 52, 104 are the factors of 104

3.How to solve √114?

By long division and approximation method, we get the value of  √114 as 10.677 
 

4.How to solve √30?

By the long division method and prime factorization method, we get the value of √30 as 5.477 (approx)
 

5.Is 104 divisible by 7?

 No 104 is not divisible by 7 
 

Important Glossaries for Square Root of 104

  • Velocity:It is a measure of how fast something is moving in a specific direction. 
  • Prime factors:Prime factors are the prime numbers that multiply together to give the original number. 

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Jaskaran Singh Saluja

About the Author

Jaskaran Singh Saluja is a math wizard with nearly three years of experience as a math teacher. His expertise is in algebra, so he can make algebra classes interesting by turning tricky equations into simple puzzles.

Fun Fact

: He loves to play the quiz with kids through algebra to make kids love it.