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Last updated on May 26th, 2025

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Square Root of 196

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The square root of 196 is a value “y” such that when “y” is multiplied by itself → y ⤫ y, the result is 196. The number 196 has a unique non-negative square root, called the principal square root.

Square Root of 196 for UK Students
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What Is the Square Root of 196?

The square root of 196 is ±14, where 14 is the positive solution of the equation x2 = 196. Finding the square root is just the inverse of squaring a number and hence, squaring 14 will result in 196. The square root of 196 is written as √196 in radical form, where the ‘√’  sign is called the “radical” sign. In exponential form, it is written as (196)1/2 
 

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Finding the Square Root of 196

We can find the square root of 196 through various methods. They are:

 

  • Prime factorization method

 

  • Long division method

 

  • Approximation/Estimation method
     
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Square Root of 196 By Prime Factorization Method


The prime factorization of 196 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 196 and then make pairs of two to get the square root.

 

So, Prime factorization of 196 = 2 ×2 ×7 ×7=14 ×14


Square root of 196= √[14 × 14] = 14

 

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Square Root of 196 By Long Division Method

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 196:


 Step 1: Write the number 196 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 1. Here, it is 1 because 12=1 < =1

 


Step 3: now divide 196 by 1 (the number we got from Step 2) such that we get 1 as a quotient, and we get a remainder.  Double the divisor 1, we get 2, and then the largest possible number A1=4 is chosen such that when 4 is written beside the new divisor 2, a 2-digit number is formed →24, and multiplying 4 with 24 gives 96, which
when subtracted from 96, gives 0.

 


Repeat this process until you reach the remainder of 0. 


 
Step 4: The quotient obtained is the square root of 196. In this case, it is 14.

 

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Square Root of 196 By Subtraction Method

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 196 and then subtract the first odd number from it. Here, in this  case, it is 196-1=195


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., 195, and again subtract the next odd number after 1, which is 3, → 195-3=192. 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 14 steps

 
So, the square root is equal to the count, i.e., the square root of 196 is ±14.

 

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Common Mistakes and How to Avoid Them in the Square Root of 196

When we find the square root of 196, we often make some key mistakes, especially when we solve problems related to that. So, let’s see some common mistakes and their solutions.

 

Mistake 1

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 Incorrectly applying the square root property

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Square root do not distribute over additions. For example, √196 ≠   √100+√96
 

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Square Root of 196 Examples

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Problem 1

Find √(196⤬169) ?

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√(196⤬169)

 

= 14 ⤬13

 

= 182


Answer : 182
 

Explanation

firstly, we found the values of the square roots of 196 and 169, then multiplied the values.
 

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Problem 2

What is √196 multiplied by 14 ?

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 √196 ⤬ 14

 

= 14⤬14

 

= 196


Answer: 196
 

Explanation

finding the value of √196 and multiplying by 14.
 

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Problem 3

)Find the radius of a circle whose area is 196π cm^2.

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Given, the area of the circle = 196π cm2


Now, area = πr2 (r is the radius of the circle)


So, πr2 = 196π cm2


We get, r2 = 196 cm2


r = √196 cm


Putting the value of √196 in the above equation, 


We get, r = ±14 cm


Here we will consider the positive value of 14.


Therefore, the radius of the circle is 14 cm.


Answer: 14 cm.
 

Explanation

We know that, area of a circle = πr2 (r is the radius of the circle) According to this equation, we are getting the value of “r” as 14 cm by finding the value of the square root of 196.

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Problem 4

Find the length of a side of a square whose area is 196 cm^2

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Given, the area = 196 cm2


We know that, (side of a square)2 = area of square

Or,(side of a square)2 = 196


Or,  (side of a square)= √196


Or, the side of a square = ± 14.


But, the length of a square is a positive quantity only, so, the length of the side is 14 cm.


Answer: 14 cm
 

Explanation

We know that, (side of a square)2 = area of square. Here, we are given with the area of the square, so, we can easily find out its square root because its square root is the measure of the side of the square
 

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Problem 5

Find √196 / √49

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 √196/√49

 

= 14/7  

 

= 2


Answer : 2 
 

Explanation

we firstly found out the values of √196 and √49, then divided  .

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FAQs on 196 Square Root

1.What are the factors of 196 ?

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2.Is 196 divisible by 13?

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3.Is 196 a perfect square or non-perfect square?

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4.Is the square root of 196 a rational or irrational number?

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5.Is 196 a composite number?

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6.How does learning Algebra help students in United Kingdom make better decisions in daily life?

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7.How can cultural or local activities in United Kingdom support learning Algebra topics such as Square Root of 196?

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8.How do technology and digital tools in United Kingdom support learning Algebra and Square Root of 196?

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9.Does learning Algebra support future career opportunities for students in United Kingdom?

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Important Glossaries for Square Root of 196

  • 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 

 

  • Prime Factorization:  Expressing the given expression as a product of its factors. Ex: 48=2 × 2 × 2 × 2 × 3

 

  • 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 :3, 8, 24
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About BrightChamps in United Kingdom

At BrightChamps, we believe algebra goes beyond symbols—it unlocks countless opportunities! Our mission is to help children throughout the United Kingdom develop essential math skills, focusing today on the Square Root of 196 with an emphasis on understanding square roots—in a lively, enjoyable, and straightforward way. Whether your child is figuring out the speed of a roller coaster at Alton Towers, tallying scores at a local football match, or managing their pocket money for the newest gadgets, mastering algebra gives them the confidence for everyday challenges. Our interactive lessons keep learning simple and enjoyable. Because children in the UK learn differently, we adapt our approach to fit each child’s unique needs. From the bustling streets of London to the scenic Cornish coasts, BrightChamps makes math relatable and exciting throughout the UK. Let’s bring square roots into every child’s math journey!
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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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Fun Fact

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

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