Square root of 96
2026-02-21 20:28 Diff
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Last updated on August 5, 2025

The square root of 96 is the inverse operation of squaring a value “y” such that when “y” is multiplied by itself → y ⤫ y, the result is 96. It contains both positive and a negative root, where the positive root is called the principal square root.

What Is the Square Root of 96?

The square root of 96 is ±9.79795897113. The positive value,9.79795897113 is the solution of the equation x2 = 96.

As defined, the square root is just the inverse of squaring a number, so, squaring 9.79795897113 will result in 96.  The square root of 96 is expressed as √96 in radical form, where the ‘√’  sign is called “radical”  sign. In exponential form, it is written as (96)1/2  
 

Finding the Square Root of 96

We can find the square root of 96 through various methods. They are:


Prime factorization method


Long division method


Approximation/Estimation method
 

Square Root of 96 By Prime Factorization Method

The prime factorization of 96 involves breaking down a number into its factors. Divide 96 by prime numbers, and continue to divide the quotients until they can’t be separated anymore. After factorizing 96, make pairs out of the factors to get the square root. If there exists numbers which cannot be made pairs further, we place those numbers with a “radical” sign along with the obtained pairs

So, Prime factorization of 96 = 3 × 2 ×2×2 ×2 ×2 


for 96, two pairs of factors 2 obtained, but a single 3 and a single 2 are also obtained.


So, it can be expressed as  √96 = √(3×2 ×2× 2 × 2  × 2) = 4√6


4√6 is the simplest radical form of √96
 

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Square Root of 96 by Long Division Method

This is a method 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 96:


Step 1 : Write the number 96, and draw a bar above the pair of digits from right to left.

                Step 2 : Now, find the greatest number whose square is less than or equal to 96. Here, it is9, Because 92=81 < 96

Step 3 : Now divide 96 by 9 (the number we got from Step 2) such that we get 9 as quotient, and we get a remainder. Double the divisor 9, we get 18 and then the largest possible number A1=7 is chosen such that when 7 is written beside the new divisor, 18, a 3-digit number is formed →187 and multiplying 7 with 187 gives 1309 which is less than 1500.

Repeat the process until you reach remainder 0


We are left with the remainder, 18791 (refer to the picture), after some iterations and keeping the division till here, at this point 

              Step 4 : The quotient obtained is the square root. In this case, it is 9.797…

Square Root of 96 by Approximation Method

Approximation or estimation of square root is not the exact square root, but it is an estimate.Here, through this method, an approximate value of square root is found by guessing.

Follow the steps below:


Step 1 : Identify the square roots of the perfect squares above and below 96


Below : 81→ square root of 81 = 9     ……..(i)


 Above : 100 →square root of 100= 10    ……..(ii)


Step 2 : Divide 96 with one of 9 or 10 


 If we choose 9, and divide 96 by 9, we get 10.666  …….(iii)


             
Step 3: Find the average of 9 (from (i)) and 10.666 (from (iii))


(9+10.666)/2 = 9.8333

Hence, 9.8333 is the approximate square root of 96
 

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Problem 1

Simplify 5√96 + 13√96 ?

Okay, lets begin

5√96+13√96

= √96(5+13)

= 9.797 ⤬ (5+13)

=18 ⤬ 9.797

= 176.346


Answer : 176.346
 

Explanation

Taking out the common part √96, adding the values inside bracket. √96= 9.797, so multiplying the square root value with the sum.
 

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Problem 2

Multiply √96 with √6

Okay, lets begin

 √96  ⤬ √6

= 4√6⤬ √6

=4 ⤬6

=24


Answer : 24
 

Explanation

multiplying the simplest radical form of √96 with √6.
 

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Problem 3

Compare √96 and √97

Okay, lets begin

 √96 ≅ 9.797,

√97 ≅ 9.8488


So, √97 is greater than √96


Answer: √97 > √96
 

Explanation

finding out the approximate values of √96 and √97 and comparing them
 

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Problem 4

If y=√96, find y^2

Okay, lets begin

firstly, y=√96= 9.79795897113


Now, squaring y, we get,

 
y2= (9.79795897113)2=96

or, y2=96


Answer : 96
 

Explanation

squaring “y” which is same as squaring the value of √96 resulted to 96.
 

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Problem 5

Find √96 / √48

Okay, lets begin

√96/√48

= √(96/48)

= √2

= 1.414


Answer : 1.414 
 

Explanation

dividing the square root value of 96 with that of square root value of 48.
 

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FAQs on 96 Square Root

1. How to solve √95?

√95 can be solved through various methods like Long Division Method, Prime Factorization Method or Approximation Method. The value is 9.7467943… 
 

2.Is 7 a factor of 96?

 No, 7 is not a factor of 96
 

3.Is 96 a perfect square or non-perfect square?

 96 is a non-perfect square, since 96 =(9.79795897113)2.
 

4.Is the square root of 96 a rational or irrational number?

The square root of 96 is ±9.79795897113. So, 9.79795897113 is an irrational number, since it cannot be obtained by dividing two integers and cannot be written in the form p/q, where p and q are integers.
 

5.What is the LCM of 96 and 404?

 9696 is the LCM of 96 and 404, where 9696 is the smallest number that is a multiple of both 96 and 404, and it is also the number that both 96 and 404 divide into evenly.
 

Important Glossaries for Square Root of 96

  • 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: 3 ⤬ 3 ⤬ 3 ⤬ 3 = 81 or, 34 = 81, where 3 is the base, 4 is the exponent 
  • Factorization:Expressing the given expression as a product of its factors Ex: 52=2 ⤬ 2 ⤬ 13 
  • Prime Numbers : Numbers which are greater than 1, having only 2 factors as →1 and Itself. Ex: 1,3,5,7,....
  • 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. 
  • 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 :2, 8, 18
     

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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.

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