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Last updated on May 26th, 2025

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Square Root of 1242

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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 such as vehicle design, finance, etc. Here, we will discuss the square root of 1242.

Square Root of 1242 for Thai Students
Professor Greenline from BrightChamps

What is the Square Root of 1242?

The square root is the inverse of the square of a number. 1242 is not a perfect square. The square root of 1242 is expressed in both radical and exponential form. In radical form, it is expressed as √1242, whereas in exponential form it is (1242)^(1/2). √1242 ≈ 35.2293, 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 1242

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

 

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

Square Root of 1242 by Prime Factorization Method

The product of prime factors is the prime factorization of a number. Now let us look at how 1242 is broken down into its prime factors:

 

Step 1: Finding the prime factors of 1242 Breaking it down, we get 2 x 3 x 3 x 3 x 23: 2^1 x 3^3 x 23^1

 

Step 2: Now we have found the prime factors of 1242. The next step is to make pairs of those prime factors. Since 1242 is not a perfect square, the digits of the number can’t be grouped into pairs perfectly.

 

Therefore, calculating √1242 using prime factorization is not straightforward.

Professor Greenline from BrightChamps

Square Root of 1242 by Long Division Method

The long division method is particularly used for non-perfect square numbers. In this method, we check for the closest perfect square 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 digits of 1242 from right to left. Grouping results in 12 and 42.

 

Step 2: Now we need to find a number whose square is close to or less than 12. The number is 3 because 3 squared is 9. This gives a quotient of 3, and subtracting 9 from 12 leaves a remainder of 3.

 

Step 3: Bring down 42 to make the new dividend 342. Double the current quotient to get the new divisor's base: 2 × 3 = 6.

 

Step 4: Find a digit 'n' such that 6n × n ≤ 342. By trial, 65 × 5 = 325, which is less than 342.

 

Step 5: Subtract 325 from 342, leaving a remainder of 17.

 

Step 6: Since the dividend is less than the divisor, add a decimal point to the quotient and bring down two zeros to the remainder, making it 1700.

 

Step 7: The new divisor base is 70 (from 65), and find a digit 'n' such that 70n × n ≤ 1700.

 

Step 8: Continue this process to get more decimal places.

 

So, the square root of √1242 is approximately 35.229.

Professor Greenline from BrightChamps

Square Root of 1242 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 1242 using the approximation method.

 

Step 1: Identify the closest perfect squares around 1242. The closest perfect squares are 1225 (35^2) and 1296 (36^2). Thus, √1242 falls between 35 and 36.

 

Step 2: Use the formula: (Given number - smaller perfect square) / (larger perfect square - smaller perfect square). Using the formula: (1242 - 1225) / (1296 - 1225) = 17 / 71 ≈ 0.239 Adding this to 35, the approximate square root of 1242 is 35 + 0.239 = 35.239

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Common Mistakes and How to Avoid Them in the Square Root of 1242

Students can make mistakes while finding the square root, such as forgetting about the negative square root or skipping steps in the long division method. Let's look at a few common mistakes in detail.

Mistake 1

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Forgetting about the negative square root

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It is important to remember that a number has both positive and negative square roots. However, we usually take only the positive square root since it is more commonly used in practical applications.

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

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Square Root of 1242 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 √1242?

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The area of the square is approximately 1541.16 square units.

Explanation

The area of a square = side².

The side length is given as √1242.

Area of the square = side² = √1242 × √1242 = 35.229 × 35.229 ≈ 1242

Therefore, the area of the square box is approximately 1242 square units.

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Max, the Girl Character from BrightChamps

Problem 2

A square-shaped building measuring 1242 square feet is built; if each of the sides is √1242, what will be the square feet of half of the building?

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

621 square feet

Explanation

Since the building is square-shaped, dividing the total area by 2 gives half the area.

Dividing 1242 by 2 gives 621.

So half of the building measures 621 square feet.

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Max, the Girl Character from BrightChamps

Problem 3

Calculate √1242 × 5.

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176.145

Explanation

The first step is to find the square root of 1242, which is approximately 35.229.

Then multiply 35.229 by 5.

So, 35.229 × 5 ≈ 176.145

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Max, the Girl Character from BrightChamps

Problem 4

What will be the square root of (1236 + 6)?

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The square root is 36.

Explanation

To find the square root, we first find the sum of (1236 + 6), which equals 1242.

The square root of 1242 is approximately 35.229.

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Max, the Girl Character from BrightChamps

Problem 5

Find the perimeter of the rectangle if its length ‘l’ is √1242 units and the width ‘w’ is 38 units.

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

The perimeter of the rectangle is approximately 146.458 units.

Explanation

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

Perimeter = 2 × (√1242 + 38)

= 2 × (35.229 + 38)

≈ 2 × 73.229

≈ 146.458 units.

Max from BrightChamps Praising Clear Math Explanations
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FAQ on Square Root of 1242

1.What is √1242 in its simplest form?

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2.Mention the factors of 1242.

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3.Calculate the square of 1242.

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4.Is 1242 a prime number?

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5.1242 is divisible by?

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

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7.How can cultural or local activities in Thailand support learning Algebra topics such as Square Root of 1242?

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8.How do technology and digital tools in Thailand support learning Algebra and Square Root of 1242?

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

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Professor Greenline from BrightChamps

Important Glossaries for the Square Root of 1242

  • Square root: A square root is the inverse of squaring a number. For example, 4^2 = 16, and the inverse of the square is the square root, so √16 = 4.
     
  • Irrational number: An irrational number cannot be written in the form of p/q, where q is not equal to zero and p and q are integers.
     
  • Perfect square: A number that is the square of an integer. For example, 36 is a perfect square because it can be written as 6^2.
     
  • Prime factorization: The process of expressing a number as the product of its prime factors.
     
  • Decimal: A number that includes a whole number and a fractional part, represented with a decimal point, such as 7.86, 8.65, and 9.42.
Professor Greenline from BrightChamps

About BrightChamps in Thailand

At BrightChamps, we understand algebra is more than just symbols—it opens up a world of opportunities! Our mission is to help children across Thailand develop essential math skills, focusing today on the Square Root of 1242 with a special look at square roots—in a lively, enjoyable, and easy-to-follow manner. Whether your child is discovering the speed of a roller coaster at Dream World, tallying local football scores, or managing their allowance to buy the latest gadgets, mastering algebra gives them confidence for everyday life. Our interactive lessons make learning fun and straightforward. Since children in Thailand have varied learning styles, we personalize our approach for each child. From Bangkok’s busy streets to Phuket’s tropical islands, BrightChamps brings math to life, making it relatable and exciting throughout Thailand. 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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