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Last updated on May 26th, 2025

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Square Root of 3842

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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 fields like engineering, statistics, etc. Here, we will discuss the square root of 3842.

Square Root of 3842 for Indian Students
Professor Greenline from BrightChamps

What is the Square Root of 3842?

The square root is the inverse of the square of a number. 3842 is not a perfect square. The square root of 3842 is expressed in both radical and exponential form. In the radical form, it is expressed as √3842, whereas (3842)^(1/2) in the exponential form. √3842 ≈ 61.9935, 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 3842

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 3842 by Prime Factorization Method

The product of prime factors is the prime factorization of a number. Now let us look at how 3842 is broken down into its prime factors.

 

Step 1: Finding the prime factors of 3842 Breaking it down, we find 3842 = 2 x 1921, and 1921 is 13 x 13 x 11.

 

Step 2: Now we found out the prime factors of 3842. Since 3842 is not a perfect square, the digits of the number can't be grouped in pairs.

 

Therefore, calculating 3842 using prime factorization is not straightforward.

Professor Greenline from BrightChamps

Square Root of 3842 by Long Division Method

The long division method is particularly useful 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 3842, we group it as 38 and 42.

 

Step 2: Now we need to find n whose square is less than or equal to 38. We can say n as ‘6’ because 6 x 6 = 36, which is less than 38. Now the quotient is 6, and after subtracting 36 from 38, the remainder is 2.

 

Step 3: Now let us bring down 42, making the new dividend 242. Add the old divisor with the same number: 6 + 6 = 12, which will be our new divisor.

 

Step 4: The new divisor will be 12n. We need to find the value of n.

 

Step 5: Finding 12n × n ≤ 242, let's consider n as 2, now 12 x 2 = 24.

 

Step 6: Subtract 24 from 242, the difference is 218, and the quotient is 62.

 

Step 7: Since the dividend is larger than the new divisor, we bring down two additional zeros (as decimal points) to continue the process.

 

Step 8: Continue the process to find the decimal places.

Professor Greenline from BrightChamps

Square Root of 3842 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. Let us now learn how to find the square root of 3842 using the approximation method.

 

Step 1: Now, we have to find the closest perfect square of √3842. The smallest perfect square less than 3842 is 3721 (61^2), and the largest perfect square greater than 3842 is 3969 (63^2). √3842 falls somewhere between 61 and 63.

 

Step 2: Now we apply the formula: (Given number - smallest perfect square) / (Greater perfect square - smallest perfect square) Going by the formula (3842 - 3721) / (3969 - 3721) ≈ 0.9935 Adding this to the lower bound: 61 + 0.9935 ≈ 61.9935.

 

So, the square root of 3842 is approximately 61.9935.

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Common Mistakes and How to Avoid Them in the Square Root of 3842

Students often make mistakes while finding square roots, such as forgetting about the negative square root, skipping long division steps, etc. 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 usually consider only the positive square root, as it is the required one.

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

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Square root of 3842 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 √3842?

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The area of the square is approximately 147,533 square units.

Explanation

The area of the square = side^2.

The side length is given as √3842.

Area of the square = side^2 = √3842 x √3842 ≈ 61.9935 x 61.9935 ≈ 147,533.

Therefore, the area of the square box is approximately 147,533 square units.

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Max, the Girl Character from BrightChamps

Problem 2

A square-shaped building measuring 3842 square feet is built; if each of the sides is √3842, what will be the square feet of half of the building?

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1921 square feet

Explanation

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

Dividing 3842 by 2, we get 1921.

So half of the building measures 1921 square feet.

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Max, the Girl Character from BrightChamps

Problem 3

Calculate √3842 x 5.

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Approximately 309.9675

Explanation

The first step is to find the square root of 3842, which is approximately 61.9935.

The second step is to multiply 61.9935 by 5.

So, 61.9935 x 5 ≈ 309.9675.

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Max, the Girl Character from BrightChamps

Problem 4

What will be the square root of (3842 + 158)?

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The square root is approximately 64.

Explanation

To find the square root, we need to find the sum of (3842 + 158).

3842 + 158 = 4000, and then √4000 ≈ 63.2455532.

Therefore, the square root of (3842 + 158) is approximately 64.

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Max, the Girl Character from BrightChamps

Problem 5

Find the perimeter of the rectangle if its length ‘l’ is √3842 units and the width ‘w’ is 50 units.

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

The perimeter of the rectangle is approximately 223.987 units.

Explanation

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

Perimeter = 2 × (√3842 + 50)

≈ 2 × (61.9935 + 50)

≈ 2 × 111.9935

≈ 223.987 units.

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FAQ on Square Root of 3842

1.What is √3842 in its simplest form?

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2.Mention the factors of 3842.

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3.Calculate the square of 3842.

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4.Is 3842 a prime number?

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5.3842 is divisible by?

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

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7.How can cultural or local activities in India support learning Algebra topics such as Square Root of 3842?

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8.How do technology and digital tools in India support learning Algebra and Square Root of 3842?

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

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Professor Greenline from BrightChamps

Important Glossaries for the Square Root of 3842

  • 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 a product of its prime factors.
     
  • Approximation method: A method used to find an approximate value of a number when an exact value is not needed or is difficult to obtain.
Professor Greenline from BrightChamps

About BrightChamps in India

At BrightChamps, we see algebra as more than just symbols—it opens doors to endless opportunities! Our mission is to help children all over India develop vital math skills, focusing today on the Square Root of 3842 with special attention to understanding square roots—in a way that’s engaging, lively, and easy to follow. Whether your child is calculating the speed of a passing train, keeping scores during a cricket match, or managing pocket money for the latest gadgets, mastering algebra gives them the confidence needed for everyday situations. Our interactive lessons keep learning simple and fun. As kids in India have varied learning styles, we personalize our approach to match each child. From the busy markets of Mumbai to Delhi’s vibrant streets, BrightChamps brings math to life, making it relatable and exciting throughout India. 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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