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Last updated on May 26th, 2025

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Square Root of 1154

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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 1154.

Square Root of 1154 for Omani Students
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What is the Square Root of 1154?

The square root is the inverse of the square of the number. 1154 is not a perfect square. The square root of 1154 is expressed in both radical and exponential form. In the radical form, it is expressed as √1154, whereas (1154)^(1/2) is in the exponential form. √1154 ≈ 33.962, 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 1154

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 the following methods:

 

  • Prime factorization method
     
  • Long division method
     
  • Approximation method
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Square Root of 1154 by Prime Factorization Method

The product of prime factors is the prime factorization of a number. Now let us look at how 1154 is broken down into its prime factors:

 

Step 1: Finding the prime factors of 1154 Breaking it down, we get 2 x 577. The number 577 is a prime number. Therefore, 1154 = 2 x 577.

 

Step 2: Since 1154 is not a perfect square, the digits of the number can’t be grouped in pairs. Therefore, calculating 1154 using prime factorization is not straightforward.

Professor Greenline from BrightChamps

Square Root of 1154 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 1154, we can group it as 11 and 54.

 

Step 2: Now we need to find n whose square is less than or equal to 11. We can say n is ‘3’ because 3 x 3 = 9, which is less than 11. Now, the quotient is 3, and after subtracting 9 from 11, the remainder is 2.

 

Step 3: Bring down the next group, 54, to make it 254.

 

Step 4: Double the quotient to get 6, which becomes the beginning of the new divisor.

 

Step 5: Find a digit p such that 6p x p is less than or equal to 254. In this case, p is 4 because 64 x 4 = 256, which is close to 254.

 

Step 6: Subtract 256 from 254 to get a remainder of -2, indicating a small error in selection, adjust by using a lower number.

 

Step 7: Continue with decimal values for more precision, leading to a quotient of approximately 33.96.

Professor Greenline from BrightChamps

Square Root of 1154 by Approximation Method

The approximation method is another method for finding 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 1154 using the approximation method.

 

Step 1: Now we have to find the closest perfect squares to √1154. The smallest perfect square less than 1154 is 1089 (33²) and the largest perfect square greater than 1154 is 1156 (34²). Thus, √1154 falls between 33 and 34.

 

Step 2: Apply the formula: (Given number - smallest perfect square) / (Greater perfect square - smallest perfect square) (1154 - 1089) / (1156 - 1089) = 65 / 67 ≈ 0.97 Using the formula, we identified the decimal point of our square root. Adding this to the initial estimate gives us 33 + 0.97 = 33.97, so the square root of 1154 is approximately 33.97.

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Common Mistakes and How to Avoid Them in the Square Root of 1154

Students often make mistakes while finding the square root, such as forgetting about the negative square root or skipping steps in the long division method. Now let us look at a few of those mistakes 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 has both positive and negative square roots. However, we only take the positive square root when solving real-world problems.

 

For example: √50 = 7.07, but there is also -7.07, which should not be forgotten.

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Square Root of 1154 Examples

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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 √1154?

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The area of the square is approximately 1154 square units.

Explanation

The area of the square = side².

The side length is given as √1154.

Area of the square = side² = √1154 x √1154 = 1154.

Therefore, the area of the square box is approximately 1154 square units.

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Max, the Girl Character from BrightChamps

Problem 2

A square-shaped building measuring 1154 square feet is built; if each of the sides is √1154, what will be the square feet of half of the building?

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577 square feet.

Explanation

The building is square-shaped, so we can divide the given area by 2.

Dividing 1154 by 2, we get 577.

So half of the building measures 577 square feet.

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Max, the Girl Character from BrightChamps

Problem 3

Calculate √1154 x 5.

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Approximately 169.81.

Explanation

First, find the square root of 1154, which is approximately 33.97.

Then multiply 33.97 by 5.

So, 33.97 x 5 ≈ 169.81.

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Max, the Girl Character from BrightChamps

Problem 4

What will be the square root of (1150 + 4)?

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The square root is approximately 34.

Explanation

To find the square root, we need to find the sum of (1150 + 4).

1150 + 4 = 1154, and √1154 ≈ 34.

Therefore, the square root of (1150 + 4) is approximately ±34.

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Max, the Girl Character from BrightChamps

Problem 5

Find the perimeter of the rectangle if its length ‘l’ is √1154 units and the width ‘w’ is 38 units.

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The perimeter of the rectangle is approximately 143.94 units.

Explanation

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

Perimeter = 2 × (√1154 + 38) = 2 × (33.97 + 38) ≈ 2 × 71.97 ≈ 143.94 units.

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FAQ on Square Root of 1154

1.What is √1154 in its simplest form?

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2.Mention the factors of 1154.

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3.Calculate the square of 1154.

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4.Is 1154 a prime number?

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5.1154 is divisible by?

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

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7.How can cultural or local activities in Oman support learning Algebra topics such as Square Root of 1154?

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8.How do technology and digital tools in Oman support learning Algebra and Square Root of 1154?

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

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Professor Greenline from BrightChamps

Important Glossaries for the Square Root of 1154

  • Square root: A square root is the inverse of a square. Example: 4² = 16, and the inverse of the square is the square root, which 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. This is known as the principal square root.

 

  • Prime factorization: The expression of a number as a product of its prime factors. For example, the prime factorization of 1154 is 2 x 577.

 

  • Long division method: A method used to find the square root of non-perfect squares by dividing the number into groups and subtracting iteratively to approximate the square root.
Professor Greenline from BrightChamps

About BrightChamps in Oman

At BrightChamps, we understand algebra as more than symbols—it’s a key to unlocking many opportunities! Our mission is to help children across Oman gain important math skills, focusing today on the Square Root of 1154 with special attention to square roots—in an engaging, lively, and easy-to-follow manner. Whether your child is measuring how fast a roller coaster moves at Oman’s Dreamland Aqua Park, tracking local football scores, or managing their allowance for the latest gadgets, mastering algebra gives them confidence for everyday tasks. Our hands-on lessons make learning simple and fun. Because children in Oman learn differently, we adapt lessons to fit each learner’s style. From Muscat’s vibrant city life to beautiful natural landscapes, BrightChamps brings math to life, making it exciting throughout Oman. Let’s make square roots a joyful part of 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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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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