BrightChamps Logo
Login
Creative Math Ideas Image
Live Math Learners Count Icon102 Learners

Last updated on May 26th, 2025

Math Whiteboard Illustration

Square Root of 613

Professor Greenline Explaining Math Concepts

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 various fields such as vehicle design, finance, etc. Here, we will discuss the square root of 613.

Square Root of 613 for Filipino Students
Professor Greenline from BrightChamps

What is the Square Root of 613?

The square root is the inverse of the square of a number. 613 is not a perfect square. The square root of 613 is expressed in both radical and exponential form. In radical form, it is expressed as √613, whereas in exponential form it is expressed as (613)^(1/2). √613 ≈ 24.7588, 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 613

The prime factorization method is used for perfect square numbers. However, the prime factorization method is not used for non-perfect square numbers where 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 613 by Prime Factorization Method

The product of prime factors is the prime factorization of a number. Now let us look at how 613 is broken down into its prime factors:

 

Step 1: Finding the prime factors of 613. 613 is a prime number itself, so it cannot be broken down into smaller prime factors. Since 613 is not a perfect square, calculating √613 using prime factorization is not possible.

Professor Greenline from BrightChamps

Square Root of 613 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: Start by grouping the numbers from right to left. In the case of 613, the grouping remains as 613.

 

Step 2: Find the largest integer n such that n² is less than or equal to 6. n = 2 because 2² = 4, which is less than 6. The quotient is 2, and the remainder is 6 - 4 = 2.

 

Step 3: Bring down the next pair of digits (13) to get 213. Double the quotient 2 to get 4 as the starting digit of the new divisor.

 

Step 4: Determine n such that 4n × n ≤ 213. n = 5 because 45 × 5 = 225, which is greater than 213. Therefore, n = 4.

 

Step 5: Subtract 204 (44 × 4) from 213 to get 9 as the remainder. Add a decimal point and bring down the next pair of zeros to make it 900.

 

Step 6: The new divisor is 48n, and find n such that 48n × n ≤ 900. n = 1 because 481 × 1 = 481, and subtracting gives a remainder of 419.

 

Step 7: Continue this process to refine the answer to two decimal places. The square root of √613 is approximately 24.7588.

Professor Greenline from BrightChamps

Square Root of 613 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 learn how to find the square root of 613 using the approximation method.

 

Step 1: Identify the closest perfect squares to 613. The smallest perfect square less than 613 is 576 (24²), and the largest perfect square less than 625 is (25²).

 

Step 2: Since 613 is between 576 and 625, √613 is between 24 and 25.

 

Step 3: Use linear approximation or trial and error to narrow down the square root further. For example, testing values between 24 and 25 gives √613 ≈ 24.7588.

Max Pointing Out Common Math Mistakes

Common Mistakes and How to Avoid Them in the Square Root of 613

Students sometimes 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

Red Cross Icon Indicating Mistakes to Avoid in This Math Topic

Forgetting about the negative square root

Green Checkmark Icon Indicating Correct Solutions in This Math Topic

It is important to remember that a number has both positive and negative square roots. However, we typically consider only the positive square root, as it is the required one in most real-world applications.

 

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

Max from BrightChamps Saying "Hey"

Square root of 613 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 √613?

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

The area of the square is approximately 613 square units.

Explanation

The area of a square = side².

The side length is given as √613.

Area of the square = side² = √613 × √613 = 613.

Therefore, the area of the square box is approximately 613 square units.

Max from BrightChamps Praising Clear Math Explanations
Max, the Girl Character from BrightChamps

Problem 2

A square-shaped building measuring 613 square feet is built. If each of the sides is √613, what will be the square feet of half of the building?

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

306.5 square feet

Explanation

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

Dividing 613 by 2, we get 306.5.

So half of the building measures 306.5 square feet.

Max from BrightChamps Praising Clear Math Explanations
Max, the Girl Character from BrightChamps

Problem 3

Calculate √613 × 5.

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

Approximately 123.794

Explanation

First, find the square root of 613, which is approximately 24.7588. Then multiply 24.7588 by 5. So 24.7588 × 5 ≈ 123.794.

Max from BrightChamps Praising Clear Math Explanations
Max, the Girl Character from BrightChamps

Problem 4

What will be the square root of (613 + 12)?

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

The square root is approximately 25.

Explanation

To find the square root, first find the sum of (613 + 12). 613 + 12 = 625, and then √625 = 25. Therefore, the square root of (613 + 12) is ±25.

Max from BrightChamps Praising Clear Math Explanations
Max, the Girl Character from BrightChamps

Problem 5

Find the perimeter of the rectangle if its length ‘l’ is √613 units and the width ‘w’ is 20 units.

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

The perimeter of the rectangle is approximately 89.52 units.

Explanation

Perimeter of the rectangle = 2 × (length + width). Perimeter = 2 × (√613 + 20) = 2 × (24.7588 + 20) ≈ 2 × 44.7588 ≈ 89.52 units.

Max from BrightChamps Praising Clear Math Explanations
Ray Thinking Deeply About Math Problems

FAQ on Square Root of 613

1.What is √613 in its simplest form?

Math FAQ Answers Dropdown Arrow

2.Mention the factors of 613.

Math FAQ Answers Dropdown Arrow

3.Calculate the square of 613.

Math FAQ Answers Dropdown Arrow

4.Is 613 a prime number?

Math FAQ Answers Dropdown Arrow

5.Is 613 divisible by any number other than 1 and itself?

Math FAQ Answers Dropdown Arrow

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

Math FAQ Answers Dropdown Arrow

7.How can cultural or local activities in Philippines support learning Algebra topics such as Square Root of 613?

Math FAQ Answers Dropdown Arrow

8.How do technology and digital tools in Philippines support learning Algebra and Square Root of 613?

Math FAQ Answers Dropdown Arrow

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

Math FAQ Answers Dropdown Arrow
Professor Greenline from BrightChamps

Important Glossaries for the Square Root of 613

  • Square root: A square root of a number is a value that, when multiplied by itself, gives the original number. Example: √16 = 4 because 4 × 4 = 16.

 

  • Irrational number: An irrational number cannot be expressed as a simple fraction. Its decimal goes on forever without repeating. Example: √2 is irrational.

 

  • Long division method: A technique for finding the square root of a number by dividing it into smaller, more manageable parts.

 

  • Prime number: A prime number has only two factors: 1 and itself. Example: 613 is a prime number.

 

  • Approximation method: A method used to find an approximate value of a square root, often by comparing it to known perfect squares.
Professor Greenline from BrightChamps

About BrightChamps in Philippines

At BrightChamps, we believe algebra is more than symbols—it’s a gateway to countless opportunities! Our mission is to support children across the Philippines in mastering key math skills, focusing today on the Square Root of 613 with an emphasis on understanding square roots—in a lively, fun, and easy-to-follow way. Whether your child is calculating the speed of a roller coaster at Enchanted Kingdom, tracking basketball scores, or managing their allowance to buy the latest gadgets, mastering algebra builds their confidence for daily challenges. Our hands-on lessons make learning simple and enjoyable. Since kids in the Philippines learn in different styles, we tailor our approach to each learner. From Manila’s busy streets to the beautiful islands of Palawan, BrightChamps brings math to life, making it exciting and relevant throughout the Philippines. Let’s make square roots a fun part of every child’s math journey!
Math Teacher Background Image
Math Teacher Image

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.

Math Teacher Fun Facts Image
Max, the Girl Character from BrightChamps

Fun Fact

: He loves to play the quiz with kids through algebra to make kids love it.

INDONESIA - Axa Tower 45th floor, JL prof. Dr Satrio Kav. 18, Kel. Karet Kuningan, Kec. Setiabudi, Kota Adm. Jakarta Selatan, Prov. DKI Jakarta
INDIA - H.No. 8-2-699/1, SyNo. 346, Rd No. 12, Banjara Hills, Hyderabad, Telangana - 500034
SINGAPORE - 60 Paya Lebar Road #05-16, Paya Lebar Square, Singapore (409051)
USA - 251, Little Falls Drive, Wilmington, Delaware 19808
VIETNAM (Office 1) - Hung Vuong Building, 670 Ba Thang Hai, ward 14, district 10, Ho Chi Minh City
VIETNAM (Office 2) - 143 Nguyễn Thị Thập, Khu đô thị Him Lam, Quận 7, Thành phố Hồ Chí Minh 700000, Vietnam
Dubai - BrightChamps, 8W building 5th Floor, DAFZ, Dubai, United Arab Emirates
UK - Ground floor, Redwood House, Brotherswood Court, Almondsbury Business Park, Bristol, BS32 4QW, United Kingdom