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Last updated on May 26th, 2025

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Square root of 168

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If a number is multiplied by the same number, the result is a square. The inverse of the square is a square root. The square root is used in the field of vehicle design, finance etc. Here, we will discuss the square root of 168.

Square root of 168 for Canadian Students
Professor Greenline from BrightChamps

What is the square root of 168?

The square root is the inverse of the square of the number. 168 is not a perfect square. The square root of 168 is expressed in both radical and exponential form. In the radical form it is expressed as, √168 ,  whereas (168)1/2 in the exponential form. √168  = 12.96148, which is an irrational number because it cannot be expressed in the form of p/q, where p and q are integers and q ≠ 0.

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Finding the square root of 168

The prime factorization method is used for perfect square numbers. However, the prime factorization method is not used for non-perfect square numbers where long-division method and approximation method are used. Let us now learn

  

  • Prime factorization method
  • Long division method 
  • Approximation method 
     
Professor Greenline from BrightChamps

Square Root of 168 by Prime Factorization Method

The product of prime factors is the Prime factorization of a number. Now let us look at how 168 is broken down into its prime factors 

 

Step 1: Finding the prime factors of 168

 

Breaking it down, we get 2 x 2 x 2 x 3 x 7:  23  x 31  x 71

 


Step 2: Now we found out the prime factors of 168. The second step is to make pairs of those prime factors. Since 168 is not a perfect square, therefore the digits of the number can’t be grouped in pair. Therefore, calculating 168  using prime factorization is impossible.
 

Professor Greenline from BrightChamps

Square Root of 168 by Long Division Method

The long division method is particularly used for non-perfect square numbers. In this method, we should check the closest perfect square number for the given number. Let us now learn how to find the square root using the long division method, step by step

 

Step 1: To begin with, we need to group the numbers from right to left. In the case of 168, we need to group it as 68 and 1. 


Step 2: Now we need to find n whose square is 1. We can say n as ‘1’ because 1 1 is lesser than or equal to 1. Now the quotient is 1 after subtracting 1-1 the remainder is 0.


Step 3: Now let us bring down 68 which is the new dividend. Add the old divisor with the same number 1 + 1 we get 2 which will be our new divisor. 

 

Step 4: The new divisor will be the sum of the dividend and quotient. Now we get 2n as the new divisor, we need to find the value of n.

 

Step 5: The next step is finding 2 n × n ≤ 68 let us consider n as 2, now 22 x  2 = 44

 

Step 6: Subtract 68 from 44 the difference is 24, and the quotient is 12

 

Step 7: Since the dividend is less than the divisor, we need to add a decimal point. Adding the decimal point allows us to add two zeroes to the dividend. Now the new dividend is 2400.

 

Step 8: Now we need to find the new divisor that is 9 because 249 ✖ 9 = 2241 

 

Step 9: Subtracting 2241 from 2400 we get the result 159.

 

Step 10: Now the quotient is 12.9

 

Step 11: Continue doing these steps until we get two numbers after the decimal point. Suppose if there is no decimal values continue till the remainder is zero

 

So the square root of √168  is 12. 96

Professor Greenline from BrightChamps

Square root of 168 by approximation method

Approximation method is another method for finding the square roots, it is an easy method to find the square root of a given number. Now let us learn how to find the square root of 168  using the approximation method

 

Step 1: Now we have to find the closest perfect square of √168 

 

The smallest perfect square of 168 is 144 and the largest perfect square of 168 is 169. √168  falls somewhere between 12 and 13

 

Step 2: Now we need to apply the formula that is (Given number - smallest perfect square) (Greater perfect square - smallest perfect square)

 

Going by the formula (168 - 144)  ÷ (169-144) = 0.96

 

Using the formula we identified the decimal point of our square root. The next step is adding the value we got initially to the decimal number which is 12 + 0.96 = 12.96, so the square root of 168 is 12.96

 

12 + 0.96 = 12.96, so the square root of 168 is 12.96
 

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Common Mistakes and How to Avoid Them in the Square Root of 168

Students do make mistakes while finding the square root, likewise forgetting about the negative square root. Skipping long division methods etc. Now let us look at a few of those mistakes that students tend to make in detail.
 

Mistake 1

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Forgetting about negative square root
 

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It is important to make students aware that a number does have both positive and negative square roots. However, we will be taking only the positive square root, as it is the required one. For example: √50 = 7.07, there is also -7.07 which should not be forgotten.

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Square root of 168 Examples

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Max, the Girl Character from BrightChamps

Problem 1

A square-shaped room is 168 square feet, calculate the length of each side of the room.

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The length of each side of the room is 12.96 square feet
 

Explanation

 To calculate the length of the side of the room, we need to calculate the square root of 168

√168  = 12.96

This tells us the length of the side of the square room is 12.96 square feet
 

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Max, the Girl Character from BrightChamps

Problem 2

A square shaped building measuring 168 square feet is built; if each sides is √168 , what will be the square feet of half of the building?

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 84 square meters
 

Explanation

We can just divide given area by 2 as the building is square shaped


Dividing 168 by 2 = we get 84

 

So half of the building measures 84 square meters
 

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Problem 3

Calculate √168 x √5?

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64.8
 

Explanation

 The first step is to find the square root of 168 which is 12.96, the second step is to multiply 12.96 with 5

So 12.96 x 5  = 64.8
 

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Max, the Girl Character from BrightChamps

Problem 4

√168 Can this be expressed as a fraction?

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Yes, it can be expressed as a fraction

 


 

Explanation

we can express the square root of 168 as a fraction, as it is a irrational number

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Max, the Girl Character from BrightChamps

Problem 5

Identify the length of the side of the square table if the area is 168 square feet.

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12.96 square feet
 

Explanation

To calculate the side of the table we need to identify the square root of 168 that is 168 = 12.96

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FAQ on square root of 168

1.What is √168 in its simplest form?

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2.Mention the factors of 168.

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3.Calculate the square of 168.

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4.Is 168 a prime number?

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5.168 is divisible by?

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

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7.How can cultural or local activities in Canada support learning Algebra topics such as Square root of 168?

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8.How do technology and digital tools in Canada support learning Algebra and Square root of 168?

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

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Professor Greenline from BrightChamps

Important Glossaries for the Square Root of 168

  • Square root: A square root is the Inverse of a square .Example: 42 =16   and the inverse of square is square root that is  √ 16 = 4

 

  • Irrational number: An irrational number is a number that cannot be written in the form of p/q, q is not equal to zero and p and q are integers.

 

  • Principal square root: A number has both positive and negative square roots, however, it is always a positive square root that has more prominence due to its uses in the real world. That is the reason it is also known as a principal square root.

 

  • Integers: The combination of whole numbers and negative numbers are integers for example: -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6,7………….are integers

 

  • Decimal: If a number has a whole number and a fraction in a single number then it is called a decimal for example: 7.86, 8.65, and 9.42 are decimals
Professor Greenline from BrightChamps

About BrightChamps in Canada

At BrightChamps, we know algebra is more than just symbols—it’s a key to open many doors! Our aim is to support kids across Canada in grasping important math skills, such as today’s focus on the Square root of 168, highlighting square roots in a fun, engaging, and easy-to-understand way. Whether your child is measuring how fast a roller coaster moves at Canada’s Wonderland, tracking hockey scores, or planning their allowance for the latest gadgets, mastering algebra helps build their confidence for daily tasks. Our hands-on lessons make learning enjoyable and straightforward. Since kids in Canada learn in diverse ways, we tailor lessons to their individual style. From Toronto’s busy streets to British Columbia’s stunning landscapes, BrightChamps brings math to life across Canada. Let’s make square roots a fun part of your child’s math experience!
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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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