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Last updated on May 26th, 2025

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Square Root of 11849

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If a number is multiplied by itself, the result is a square. The inverse of the square is a square root. The square root is used in various fields such as vehicle design, finance, etc. Here, we will discuss the square root of 11849.

Square Root of 11849 for US Students
Professor Greenline from BrightChamps

What is the Square Root of 11849?

The square root is the inverse of squaring a number. 11849 is a perfect square. The square root of 11849 can be expressed in both radical and exponential form. In the radical form, it is expressed as √11849, whereas in exponential form it is expressed as (11849)(1/2). √11849 = 109, 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 11849

The prime factorization method is used for perfect square numbers. For non-perfect squares, methods like the long division method and approximation method are used. Let us now learn the following methods:

 

  1. Prime factorization method
  2. Long division method
  3. Approximation method
Professor Greenline from BrightChamps

Square Root of 11849 by Prime Factorization Method

The product of prime factors is the prime factorization of a number. Now let us look at how 11849 is broken down into its prime factors.

 

Step 1: Finding the prime factors of 11849 Breaking it down, we get 109 × 109.

 

Step 2: Now we found out the prime factors of 11849. Since 11849 is a perfect square, the digits of the number can be grouped in pairs.

 

Therefore, the square root of 11849 using prime factorization is 109.

Professor Greenline from BrightChamps

Square Root of 11849 by Long Division Method

The long division method is particularly used for both perfect and non-perfect square numbers. Let's 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 11849, we group it as 11, 84, and 9.

 

Step 2: Find a number whose square is less than or equal to 11. We can select 3, as 3 × 3 = 9 is less than 11. The initial quotient is 3, and after subtracting 9 from 11, the remainder is 2.

 

Step 3: Bring down the next pair of digits (84) to get a new dividend of 284. Double the quotient (3) to get a new divisor base of 6.

 

Step 4: Select a digit (4) such that 64 × 4 ≤ 284. 64 × 4 = 256, which is less than 284. Subtract 256 from 284 to get a remainder of 28.

 

Step 5: Bring down the next pair of digits (9) to get a new dividend of 289.

 

Step 6: Double the part of the quotient found so far (34) to get 68 and find a digit (1) such that 681 × 1 = 681 is less than or equal to 289. Subtract 681 from 289 to get a remainder of zero.

 

Step 7: As the remainder is zero, the square root of 11849 is 109.

Professor Greenline from BrightChamps

Square Root of 11849 by Approximation Method

The approximation method is another way to find square roots. It is an easy method to find the square root of a given number. Let's learn how to find the square root of 11849 using the approximation method.

 

Step 1: Identify two perfect squares between which 11849 lies. The smaller perfect square is 10404 (102^2), and the larger perfect square is 11664 (1082). √11849 falls between 108 and 109.

 

Step 2: Use interpolation to approximate the square root: (11849 - 11664) / (11881 - 11664) = 0.5 Adding this to 108, we get 108 + 0.5 = 108.5, which is an approximation. The exact value, however, is 109.

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Common Mistakes and How to Avoid Them in the Square Root of 11849

Students often make mistakes while finding square roots, such as forgetting about the negative square root or skipping steps in the long division method. Here are a few common mistakes in detail.

Mistake 1

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Forgetting about the negative square root

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It's important to remember that every positive number has both positive and negative square roots. However, typically only the positive square root is used in most real-world applications. For example, √49 = 7, but there's also -7, which should not be overlooked.

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Square Root of 11849 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 √11849?

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The area of the square is 11849 square units.

Explanation

The area of a square = side2.

 

The side length is given as √11849.

 

Area of the square = (√11849) × (√11849) = 11849.

 

Therefore, the area of the square box is 11849 square units.

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Max, the Girl Character from BrightChamps

Problem 2

A square-shaped building measuring 11849 square feet is built; if each of the sides is √11849, what will be the square feet of half of the building?

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5924.5 square feet

Explanation

To find half the area of the building, divide the total area by 2.

 

Dividing 11849 by 2 gives us 5924.5.

 

So half of the building measures 5924.5 square feet.

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Max, the Girl Character from BrightChamps

Problem 3

Calculate √11849 x 5.

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545

Explanation

The first step is to find the square root of 11849, which is 109.

 

The second step is to multiply 109 by 5.

 

So 109 × 5 = 545.

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Max, the Girl Character from BrightChamps

Problem 4

What will be the square root of (11849 + 0)?

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The square root is 109.

Explanation

To find the square root, sum (11849 + 0) = 11849, and then √11849 = 109.

 

Therefore, the square root of (11849 + 0) is ±109.

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Max, the Girl Character from BrightChamps

Problem 5

Find the perimeter of the rectangle if its length ‘l’ is √11849 units and the width ‘w’ is 38 units.

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The perimeter of the rectangle is 294 units.

Explanation

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

 

Perimeter = 2 × (√11849 + 38) = 2 × (109 + 38) = 2 × 147 = 294 units.

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FAQ on Square Root of 11849

1.What is √11849 in its simplest form?

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2.Mention the factors of 11849.

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3.Calculate the square of 11849.

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4.Is 11849 a prime number?

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5.11849 is divisible by?

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

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7.How can cultural or local activities in United States support learning Algebra topics such as Square Root of 11849?

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8.How do technology and digital tools in United States support learning Algebra and Square Root of 11849?

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

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Professor Greenline from BrightChamps

Important Glossaries for the Square Root of 11849

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

 

  • Perfect square: A perfect square is an integer that is the square of an integer. For example, 16 is a perfect square because it is 4 squared.

 

  • Rational number: A rational number is a number that can be expressed as the quotient or fraction p/q, where p and q are integers and q is not zero.

 

  • Integer: Integers are a set of numbers that include all whole numbers and their negatives. For example, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7, etc., are integers.

 

  • Approximation: Approximation is a method of finding a number that is close enough to the correct answer, usually within a specified range.
Professor Greenline from BrightChamps

About BrightChamps in United States

At BrightChamps, we understand algebra is more than just symbols—it’s a gateway to endless possibilities! Our goal is to empower kids throughout the United States to master key math skills, like today’s topic on the Square Root of 11849, with a special emphasis on understanding square roots—in an engaging, fun, and easy-to-grasp manner. Whether your child is calculating how fast a roller coaster zooms through Disney World, keeping track of scores during a Little League game, or budgeting their allowance for the latest gadgets, mastering algebra boosts their confidence to tackle everyday problems. Our hands-on lessons make learning both accessible and exciting. Since kids in the USA learn in diverse ways, we customize our methods to suit each learner’s style. From the lively streets of New York City to the sunny beaches of California, BrightChamps brings math alive, making it meaningful and enjoyable all across America. Let’s make square roots an exciting part of every child’s math adventure!
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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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