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Last updated on May 26th, 2025

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Square Root of 634

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If a number is multiplied by itself, the result is a square. The inverse operation of squaring is finding the square root. Square roots are applicable in various fields such as vehicle design, finance, etc. Here, we will discuss the square root of 634.

Square Root of 634 for Thai Students
Professor Greenline from BrightChamps

What is the Square Root of 634?

The square root is the inverse of squaring a number. 634 is not a perfect square. The square root of 634 is expressed in both radical and exponential form. In the radical form, it is expressed as √634, whereas in exponential form it is (634)^(1/2). √634 ≈ 25.192, 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 634

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 634 by Prime Factorization Method

The product of prime factors is the prime factorization of a number. Now let us look at how 634 is broken down into its prime factors:

 

Step 1: Finding the prime factors of 634 Breaking it down, we get 2 x 317: 2^1 x 317^1

 

Step 2: Now we found out the prime factors of 634. The next step is to make pairs of those prime factors. Since 634 is not a perfect square, the digits of the number can’t be grouped into pairs.

 

Therefore, calculating 634 using prime factorization results in an approximation.

Professor Greenline from BrightChamps

Square Root of 634 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 634, we group it as 34 and 6.

 

Step 2: Now we need to find n whose square is less than or equal to 6. We can say n as ‘2’ because 2 x 2 = 4, which is less than 6. Now the quotient is 2, and after subtracting, 6 - 4, the remainder is 2.

 

Step 3: Bring down 34 to make the new dividend 234.

 

Step 4: Add the previous divisor with the same number, 2 + 2 = 4, which will be our new divisor.

 

Step 5: Find 4n × n ≤ 234. Let us consider n as 5, now 45 x 5 = 225.

 

Step 6: Subtract 234 from 225; the remainder is 9, and the quotient is 25.

 

Step 7: Since the dividend is less than the divisor, add a decimal point and bring down two zeros to make it 900.

 

Step 8: Find the new divisor; 50 because 501 x 1 = 501.

 

Step 9: Subtract 501 from 900 to get a remainder of 399.

 

Step 10: The quotient is 25.1

 

Step 11: Continue these steps until you achieve the desired decimal precision.

 

So the square root of √634 is approximately 25.192

Professor Greenline from BrightChamps

Square Root of 634 by Approximation Method

The approximation method is another method for finding the 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 634 using the approximation method.

 

Step 1: Find the closest perfect squares around √634 The closest perfect squares are 625 and 676, with √634 falling between 25 and 26.

 

Step 2: Apply the formula: (Given number - smallest perfect square) / (Greater perfect square - smallest perfect square) Using the formula: (634 - 625) / (676 - 625) = 9 / 51 ≈ 0.176 Add the approximation to the smaller square root: 25 + 0.176 = 25.176, so the square root of 634 is approximately 25.176.

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Common Mistakes and How to Avoid Them in the Square Root of 634

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. 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's important to remember that numbers have both positive and negative square roots. However, we typically consider only the positive square root in practical applications. For instance: √25 = 5, but there is also -5 which should not be forgotten.

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Square Root of 634 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 √634?

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The area of the square is approximately 401.44 square units.

Explanation

The area of the square = side^2.

The side length is given as √634.

Area of the square = side^2 = √634 x √634 = 25.192 x 25.192 ≈ 634.367

Therefore, the area of the square box is approximately 634.367 square units.

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Max, the Girl Character from BrightChamps

Problem 2

A square-shaped building measuring 634 square feet is built; if each of the sides is √634, what will be the square feet of half of the building?

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317 square feet

Explanation

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

Dividing 634 by 2 = 317

So half of the building measures 317 square feet.

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Max, the Girl Character from BrightChamps

Problem 3

Calculate √634 x 5.

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Approximately 125.96

Explanation

First, find the square root of 634, which is approximately 25.192.

Then multiply 25.192 by 5.

So 25.192 x 5 ≈ 125.96

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Max, the Girl Character from BrightChamps

Problem 4

What will be the square root of (634 + 6)?

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The square root is approximately 25.87

Explanation

To find the square root, first calculate the sum 634 + 6 = 640.

Then √640 ≈ 25.87.

Therefore, the square root of (634 + 6) is approximately ±25.87.

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Max, the Girl Character from BrightChamps

Problem 5

Find the perimeter of the rectangle if its length ‘l’ is √634 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 126.384 units.

Explanation

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

Perimeter = 2 × (√634 + 38)

= 2 × (25.192 + 38)

= 2 × 63.192

≈ 126.384 units.

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FAQ on Square Root of 634

1.What is √634 in its simplest form?

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2.Mention the factors of 634.

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3.Calculate the square of 634.

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4.Is 634 a prime number?

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5.634 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 634?

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8.How do technology and digital tools in Thailand support learning Algebra and Square Root of 634?

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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 634

  • Square root: A square root is the inverse of squaring a number. For example, if 5^2 = 25, then √25 = 5.
     
  • 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 is 6^2.
     
  • Decimal: A number expressed in the scale of tens, often used to represent non-whole numbers. For example, 25.192 is a decimal.
     
  • Approximation: An approximate calculation or estimation of a value, often used in calculating non-perfect squares.
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 634 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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