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Last updated on May 26th, 2025

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Square Root of 1068

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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 1068.

Square Root of 1068 for Canadian Students
Professor Greenline from BrightChamps

What is the Square Root of 1068?

The square root is the inverse of the square of the number. 1068 is not a perfect square. The square root of 1068 is expressed in both radical and exponential form. In the radical form, it is expressed as √1068, whereas (1068)^(1/2) in the exponential form. √1068 ≈ 32.6742, 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.

Professor Greenline from BrightChamps

Finding the Square Root of 1068

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 and approximation methods are used. Let us now learn the following methods:

 

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

Square Root of 1068 by Prime Factorization Method

The product of prime factors is the prime factorization of a number. Now let us look at how 1068 is broken down into its prime factors.

 

Step 1: Finding the prime factors of 1068 Breaking it down, we get 2 x 2 x 3 x 89: 2^2 x 3 x 89

 

Step 2: Now we found out the prime factors of 1068. The second step is to make pairs of those prime factors. Since 1068 is not a perfect square, the digits of the number can’t be grouped in pairs.

 

Therefore, calculating 1068 using prime factorization is impossible.

Professor Greenline from BrightChamps

Square Root of 1068 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 1068, we need to group it as 68 and 10.

 

Step 2: Now we need to find n whose square is ≤ 10. We can say n as '3' because 3 x 3 = 9, which is less than or equal to 10. Now the quotient is 3, and after subtracting 9 from 10, the remainder is 1.

 

Step 3: Now let us bring down 68, making the new dividend 168. Add the old divisor with the same number 3 + 3 to get 6, which will be our new divisor.

 

Step 4: The new divisor will be the sum of the dividend and quotient. Now we get 6n as the new divisor, we need to find the value of n.

 

Step 5: The next step is finding 6n x n ≤ 168. Let us consider n as 2, so 62 x 2 = 124.

 

Step 6: Subtract 124 from 168, the difference is 44, and the quotient is 32.

 

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 4400.

 

Step 8: Now we need to find the new divisor, which is 649 because 649 x 6 ≈ 3894.

 

Step 9: Subtracting 3894 from 4400, we get 506.

 

Step 10: Now the quotient is 32.6.

 

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

 

So the square root of √1068 is approximately 32.67.

Professor Greenline from BrightChamps

Square Root of 1068 by Approximation Method

The 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 1068 using the approximation method.

 

Step 1: Now we have to find the closest perfect square of √1068. The smallest perfect square less than 1068 is 1024 and the largest perfect square greater than 1068 is 1089. √1068 falls somewhere between 32 and 33.

 

Step 2: Now we need to apply the formula that is (Given number - smallest perfect square) / (Greater perfect square - smallest perfect square). Using the formula (1068 - 1024) / (1089 - 1024) = 44 / 65 ≈ 0.6769. 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 32 + 0.6769 = 32.6769.

 

So the square root of 1068 is approximately 32.68.

Max Pointing Out Common Math Mistakes

Common Mistakes and How to Avoid Them in the Square Root of 1068

Students do make mistakes while finding the square root, such as forgetting about the negative square root and skipping long division methods. 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 the 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 1068 Examples

Ray, the Character from BrightChamps Explaining Math Concepts
Max, the Girl Character from BrightChamps

Problem 1

Can you help Max find the area of a square box if its side length is given as √1068?

Ray, the Boy Character from BrightChamps Saying "Let’s Begin"

The area of the square is 1068 square units.

Explanation

The area of the square = side^2.

The side length is given as √1068.

Area of the square = side^2

= √1068 x √1068

= 1068.

Therefore, the area of the square box is 1068 square units.

Max from BrightChamps Praising Clear Math Explanations
Max, the Girl Character from BrightChamps

Problem 2

A square-shaped building measuring 1068 square feet is built; if each of the sides is √1068, what will be the square feet of half of the building?

Ray, the Boy Character from BrightChamps Saying "Let’s Begin"

534 square feet

Explanation

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

Dividing 1068 by 2, we get 534.

So half of the building measures 534 square feet.

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Max, the Girl Character from BrightChamps

Problem 3

Calculate √1068 x 5.

Ray, the Boy Character from BrightChamps Saying "Let’s Begin"

163.37

Explanation

The first step is to find the square root of 1068, which is approximately 32.67.

The second step is to multiply 32.67 with 5.

So 32.67 x 5 = 163.35.

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Max, the Girl Character from BrightChamps

Problem 4

What will be the square root of (1089 - 21)?

Ray, the Boy Character from BrightChamps Saying "Let’s Begin"

The square root is 32.

Explanation

To find the square root, we need to find the difference (1089 - 21).

1089 - 21 = 1068, and then √1068 ≈ 32.68.

Therefore, the square root of (1089 - 21) is approximately ±32.68.

Max from BrightChamps Praising Clear Math Explanations
Max, the Girl Character from BrightChamps

Problem 5

Find the perimeter of the rectangle if its length 'l' is √1068 units and the width 'w' is 38 units.

Ray, the Boy Character from BrightChamps Saying "Let’s Begin"

We find the perimeter of the rectangle as 141.34 units.

Explanation

Perimeter of the rectangle = 2 × (length + width).

Perimeter = 2 × (√1068 + 38)

= 2 × (32.67 + 38)

= 2 × 70.67

= 141.34 units.

Max from BrightChamps Praising Clear Math Explanations
Ray Thinking Deeply About Math Problems

FAQ on Square Root of 1068

1.What is √1068 in its simplest form?

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2.Mention the factors of 1068.

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3.Calculate the square of 1068.

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4.Is 1068 a prime number?

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5.1068 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 1068?

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8.How do technology and digital tools in Canada support learning Algebra and Square Root of 1068?

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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 1068

  • Square root: A square root is the inverse of a square. Example: 4^2 = 16 and the inverse of the square is the square root, that is √16 = 4.
     
  • Irrational number: An irrational number is a number that cannot be written in the form of p/q, where 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 the positive square root that has more prominence due to its uses in the real world. That is the reason it is also known as the principal square root.
     
  • Prime factorization: The process of expressing a number as the product of its prime factors.
     
  • Approximation method: A method used to estimate the value of a square root by finding the nearest perfect squares.
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 1068, 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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Max, the Girl Character from BrightChamps

Fun Fact

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

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