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Last updated on May 26th, 2025

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Square Root of 1369

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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 1369.

Square Root of 1369 for Canadian Students
Professor Greenline from BrightChamps

What is the Square Root of 1369?

The square root is the inverse of the square of the number. 1369 is a perfect square. The square root of 1369 is expressed in both radical and exponential form. In the radical form, it is expressed as √1369, whereas in exponential form it is expressed as (1369)^(1/2). √1369 = 37, which is a rational number because it can 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 1369

The prime factorization method is used for perfect square numbers. Since 1369 is a perfect square, we can use the prime factorization method. However, for non-perfect square numbers, long-division and approximation methods are used. Let us now learn the following methods:

 

  • Prime factorization method
  • Long division method
  • Approximation method
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Square Root of 1369 by Prime Factorization Method

The product of prime factors is the prime factorization of a number. Now let us look at how 1369 is broken down into its prime factors.

 

Step 1: Finding the prime factors of 1369

 

Breaking it down, we get 37 x 37: 37^2

 

Step 2: Now we found out the prime factors of 1369. Since 1369 is a perfect square, the digits of the number can be grouped in pairs. Therefore, calculating 1369 using prime factorization is straightforward, and the square root is 37.

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Square Root of 1369 by Long Division Method

The long division method can also be used for 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 1369, the grouping is not needed as it naturally forms pairs.

 

Step 2: Now we need to find n whose square is closest to 13. We can say n as '3' because 3 x 3 = 9 is lesser than or equal to 13. Now the quotient is 3, after subtracting 9 from 13 the remainder is 4.

 

Step 3: Bring down 69, which is the new dividend. Double the quotient to get the new divisor, 6.

 

Step 4: The new divisor is now 6n. Find the largest n such that 6n * n is less than or equal to 469.

 

Step 5: Try n = 7, so 67 x 7 = 469.

 

Step 6: Subtract 469 from 469, the remainder is 0, and the quotient is 37. Therefore, the square root of 1369 is 37.

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Square Root of 1369 by Approximation Method

The approximation method is another method for finding the square roots, and it is an easy method to find the square root of a given number. However, since 1369 is a perfect square, this method is not necessary.

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Common Mistakes and How to Avoid Them in the Square Root of 1369

Students do make mistakes while finding the square root, such as 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.

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Square root of 1369 Examples

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Problem 1

Can you help Max find the area of a square box if its side length is given as √1369?

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The area of the square is 1369 square units.

Explanation

The area of the square = side^2.

The side length is given as √1369.

Area of the square = side^2 = √1369 x √1369 = 37 x 37 = 1369.

Therefore, the area of the square box is 1369 square units.

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Max, the Girl Character from BrightChamps

Problem 2

A square-shaped building measuring 1369 square feet is built; if each of the sides is √1369, what will be the square feet of half of the building?

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684.5 square feet

Explanation

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

Dividing 1369 by 2 = we get 684.5.

So half of the building measures 684.5 square feet.

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Max, the Girl Character from BrightChamps

Problem 3

Calculate √1369 x 5.

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185

Explanation

The first step is to find the square root of 1369, which is 37.

The second step is to multiply 37 by 5. So 37 x 5 = 185.

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Problem 4

What will be the square root of (1360 + 9)?

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The square root is 37

Explanation

To find the square root, we need to find the sum of (1360 + 9). 1360 + 9 = 1369, and then √1369 = 37.

Therefore, the square root of (1360 + 9) is ±37.

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Max, the Girl Character from BrightChamps

Problem 5

Find the perimeter of the rectangle if its length ‘l’ is √1369 units and the width ‘w’ is 38 units.

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The perimeter of the rectangle is 150 units.

Explanation

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

Perimeter = 2 × (√1369 + 38) = 2 × (37 + 38) = 2 × 75 = 150 units.

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FAQ on Square Root of 1369

1.What is √1369 in its simplest form?

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2.Mention the factors of 1369.

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3.Calculate the square of 1369.

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4.Is 1369 a prime number?

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5.1369 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 1369?

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8.How do technology and digital tools in Canada support learning Algebra and Square Root of 1369?

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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 1369

  • Square root: A square root is the inverse of a square. Example: 6^2 = 36, and the inverse of the square is the square root, that is, √36 = 6.

 

  • Rational number: A rational number is a number that can be written in the form of p/q, where q is not equal to zero and p and q are integers.

 

  • Perfect square: A perfect square is an integer that is the square of an integer. Example: 36 is a perfect square because it is 6^2.

 

  • Integer: An integer is a whole number that can be positive, negative, or zero. Examples: -5, 0, 3, 4.

 

  • Decimal: If a number has a whole number and a fractional part in a single number, then it is called a decimal. Examples: 7.86, 8.65, 9.42.
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 1369, 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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