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Last updated on May 26th, 2025

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Square Root of 651

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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 651.

Square Root of 651 for Thai Students
Professor Greenline from BrightChamps

What is the Square Root of 651?

The square root is the inverse of the square of a number. 651 is not a perfect square. The square root of 651 is expressed in both radical and exponential forms. In radical form, it is expressed as √651, whereas in exponential form it is (651)^(1/2). √651 ≈ 25.5147, 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.

Professor Greenline from BrightChamps

Finding the Square Root of 651

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 651 by Prime Factorization Method

The product of prime factors is the prime factorization of a number. Now let us look at how 651 is broken down into its prime factors:

 

Step 1: Finding the prime factors of 651 Breaking it down, we get 3 × 217: 3 × (7 × 31)

 

Step 2: Now we have found the prime factors of 651. Since 651 is not a perfect square, the digits of the number can’t be grouped in pairs.

 

Therefore, calculating √651 using prime factorization alone is not possible.

Professor Greenline from BrightChamps

Square Root of 651 by Long Division Method

The long division method is particularly used for non-perfect square numbers. Let us now learn how to find the square root using the long division method, step by step:

 

Step 1: To begin with, we group the numbers from right to left. For 651, group it as 51 and 6.

 

Step 2: Find n such that n² ≤ 6. We can say n = 2 because 2 × 2 = 4, which is less than 6. The quotient is 2 and the remainder is 2.

 

Step 3: Bring down 51, making the new dividend 251. Double the quotient (2), giving a new divisor of 4.

 

Step 4: Find n such that 4n × n ≤ 251. For n = 6, 46 × 6 = 276, which is more than 251. Trying n = 5, we have 45 × 5 = 225, which fits.

 

Step 5: Subtract 225 from 251, leaving a remainder of 26. The quotient is now 25.

 

Step 6: Since the remainder is less than the divisor, we add a decimal point and bring down zeros, making the new dividend 2600.

 

Step 7: Double the quotient (25), making the new divisor 50, and find n such that 50n × n ≤ 2600. Trying n = 5 gives 505 × 5 = 2525.

 

Step 8: Subtract 2525 from 2600, leaving the remainder 75. The quotient is now 25.5.

 

Step 9: Repeat the process until you achieve the desired precision.

 

The square root of 651 is approximately 25.5147.

Professor Greenline from BrightChamps

Square Root of 651 by Approximation Method

The approximation method is another way to find square roots. It is an easy method to estimate the square root of a given number. Let us learn how to find the square root of 651 using the approximation method.

 

Step 1: Find the closest perfect squares to √651. The smallest perfect square less than 651 is 625 (√625 = 25), and the largest perfect square greater than 651 is 676 (√676 = 26). Thus, √651 falls between 25 and 26.

 

Step 2: Apply the formula: (Given number - smallest perfect square) / (Greater perfect square - smallest perfect square) Using the formula: (651 - 625) / (676 - 625) = 26 / 51 ≈ 0.51 Add this result to the smaller perfect square root: 25 + 0.51 ≈ 25.51.

 

So the square root of 651 is approximately 25.51.

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Common Mistakes and How to Avoid Them in the Square Root of 651

Students may make mistakes while finding the square root, such as forgetting about the negative square root, skipping steps in the long division method, etc. Let us look at a few of these 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 often only consider 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 651 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 √651?

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The area of the square is approximately 651 square units.

Explanation

The area of the square = side².

The side length is given as √651.

Area of the square = side² = √651 × √651 = 651.

Therefore, the area of the square box is approximately 651 square units.

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Max, the Girl Character from BrightChamps

Problem 2

A square-shaped building measuring 651 square feet is built; if each of the sides is √651, what will be the square feet of half of the building?

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325.5 square feet

Explanation

Divide the given area by 2 since the building is square-shaped.

Dividing 651 by 2 gives 325.5.

So half of the building measures 325.5 square feet.

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Max, the Girl Character from BrightChamps

Problem 3

Calculate √651 × 5.

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Approximately 127.5735

Explanation

First, find the square root of 651, which is approximately 25.5147, then multiply 25.5147 by 5.

So 25.5147 × 5 ≈ 127.5735.

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Max, the Girl Character from BrightChamps

Problem 4

What will be the square root of (651 + 25)?

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The square root is approximately 26.

Explanation

To find the square root, calculate the sum of (651 + 25).

651 + 25 = 676, and then √676 = 26.

Therefore, the square root of (651 + 25) is ±26.

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Max, the Girl Character from BrightChamps

Problem 5

Find the perimeter of the rectangle if its length ‘l’ is √651 units and the width ‘w’ is 31 units.

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We find the perimeter of the rectangle as approximately 113.03 units.

Explanation

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

Perimeter = 2 × (√651 + 31)

≈ 2 × (25.5147 + 31)

≈ 2 × 56.5147

≈ 113.03 units.

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FAQ on Square Root of 651

1.What is √651 in its simplest form?

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2.Mention the factors of 651.

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3.Calculate the square of 651.

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4.Is 651 a prime number?

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5.651 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 651?

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8.How do technology and digital tools in Thailand support learning Algebra and Square Root of 651?

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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 651

  • 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 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 why it is also known as the principal square root.
     
  • Prime factorization: Breaking down a number into its basic prime numbers that multiply together to equal the original number. Example: 651 = 3 × 7 × 31.
     
  • Decimal: A number that includes a decimal point followed by digits representing a fraction, such as 25.5147.
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 651 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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