BrightChamps Logo
Login
Creative Math Ideas Image
Live Math Learners Count Icon101 Learners

Last updated on May 26th, 2025

Math Whiteboard Illustration

Square Root of 741

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 fields such as vehicle design and finance. Here, we will discuss the square root of 741.

Square Root of 741 for Singaporean Students
Professor Greenline from BrightChamps

What is the Square Root of 741?

The square root is the inverse of squaring a number. 741 is not a perfect square. The square root of 741 is expressed in both radical and exponential form. In radical form, it is expressed as √741, and in exponential form as (741)^(1/2). √741 ≈ 27.213, 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 741

The prime factorization method is used for perfect square numbers. However, for non-perfect square numbers like 741, 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 741 by Prime Factorization Method

The product of prime factors is the prime factorization of a number. Now let us look at how 741 is broken down into its prime factors.

 

Step 1: Finding the prime factors of 741

 

Breaking it down, we get 3 x 13 x 19: 3^1 x 13^1 x 19^1

 

Step 2: Now we found the prime factors of 741. Since 741 is not a perfect square, the digits of the number can’t be grouped in pairs that result in a whole number. Therefore, calculating 741 using prime factorization alone is insufficient for finding its square root.

Professor Greenline from BrightChamps

Square Root of 741 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 741, we need to group it as 41 and 7.

 

Step 2: Now we need to find n whose square is less than or equal to 7. We can say n is '2' because 2 x 2 = 4, which is less than 7. The quotient is 2, and after subtracting 4 from 7, the remainder is 3.

 

Step 3: Bring down the next pair, which is 41, to make the new dividend 341. Add the old divisor, which was 2, to itself, getting 4 as the new tentative divisor.

 

Step 4: Determine the next digit of the quotient by finding n such that 4n x n ≤ 341. Choosing n as 8, we get 48 x 8 = 384, which is too large. Trying n as 7, we get 47 x 7 = 329, which fits.

 

Step 5: Subtract 329 from 341 to get a remainder of 12.

 

Step 6: Since the dividend is less than the divisor, we need to add a decimal point. Adding the decimal point allows us to add two zeroes to the dividend, making it 1200.

 

Step 7: Repeat the process to get more decimal places. The next digit of the quotient is determined using the divisor 547. Continuing this process gives us the square root of 741 as approximately 27.213.

Professor Greenline from BrightChamps

Square Root of 741 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. Now let us learn how to find the square root of 741 using the approximation method.

 

Step 1: Identify the closest perfect squares around 741. The smallest perfect square less than 741 is 729 (27^2), and the largest perfect square greater than 741 is 784 (28^2). So, √741 falls between 27 and 28.

 

Step 2: Use the approximation formula: (Given number - smaller perfect square) ÷ (larger perfect square - smaller perfect square). Using the formula: (741 - 729) ÷ (784 - 729) = 12 ÷ 55 ≈ 0.218 Adding the approximate value to the lower bound gives: 27 + 0.218 ≈ 27.218. Therefore, the square root of 741 is approximately 27.218.

Max Pointing Out Common Math Mistakes

Common Mistakes and How to Avoid Them in the Square Root of 741

Students often make mistakes while finding square roots, such as forgetting about the negative square root or skipping steps in the long division method. Let's explore 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's important to remind students that a number has both positive and negative square roots. However, we usually consider only the positive square root in practical applications.

 

For example, √50 = 7.071, but there is also -7.071, which should not be forgotten.

Max from BrightChamps Saying "Hey"

Square Root of 741 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 √741?

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

The area of the square is approximately 549 square units.

Explanation

The area of the square = side^2.

The side length is given as √741.

Area of the square = side^2 = √741 × √741 ≈ 27.213 × 27.213 ≈ 740.752

Therefore, the area of the square box is approximately 740.752 square units.

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

Problem 2

A square-shaped building measuring 741 square feet is built; if each of the sides is √741, what will be the square feet of half of the building?

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

370.5 square feet

Explanation

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

Dividing 741 by 2, we get 370.5.

So, half of the building measures 370.5 square feet.

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

Problem 3

Calculate √741 × 5.

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

136.065

Explanation

First, find the square root of 741, which is approximately 27.213.

Then multiply 27.213 by 5.

So, 27.213 × 5 ≈ 136.065.

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

Problem 4

What will be the square root of (741 + 59)?

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

The square root is 29.

Explanation

To find the square root, first find the sum of (741 + 59). 741 + 59 = 800, and the square root of 800 is approximately ±28.284.

Therefore, the square root of (741 + 59) is approximately ±28.284.

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 √741 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 130.426 units.

Explanation

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

Perimeter = 2 × (√741 + 38) ≈ 2 × (27.213 + 38) ≈ 2 × 65.213 = 130.426 units.

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

FAQ on Square Root of 741

1.What is √741 in its simplest form?

Math FAQ Answers Dropdown Arrow

2.Mention the factors of 741.

Math FAQ Answers Dropdown Arrow

3.Calculate the square of 741.

Math FAQ Answers Dropdown Arrow

4.Is 741 a prime number?

Math FAQ Answers Dropdown Arrow

5.741 is divisible by?

Math FAQ Answers Dropdown Arrow

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

Math FAQ Answers Dropdown Arrow

7.How can cultural or local activities in Singapore support learning Algebra topics such as Square Root of 741?

Math FAQ Answers Dropdown Arrow

8.How do technology and digital tools in Singapore support learning Algebra and Square Root of 741?

Math FAQ Answers Dropdown Arrow

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

Math FAQ Answers Dropdown Arrow
Professor Greenline from BrightChamps

Important Glossaries for the Square Root of 741

  • Square Root: A square root is the inverse of squaring a number. Example: 4^2 = 16, and the inverse is the square root: √16 = 4.

 

  • Irrational Number: An irrational number cannot be expressed as a fraction p/q, where p and q are integers, and q ≠ 0.

 

  • Principal Square Root: A number has both positive and negative square roots, but the positive square root is typically used in practical applications. This is known as the principal square root.

 

  • Decimal: A decimal is a number that includes a whole number and a fractional part, such as 7.86, 8.65, and 9.42.

 

  • Long Division Method: A process used to find the square root of non-perfect squares by dividing the number into parts and estimating the quotient step by step.
Professor Greenline from BrightChamps

About BrightChamps in Singapore

At BrightChamps, we see algebra as more than just symbols—it opens up a world of opportunities! We’re committed to helping children across Singapore develop essential math skills, focusing today on the Square Root of 741 with a special focus on understanding square roots—in an engaging, lively, and simple way. Whether your child is figuring out how fast a roller coaster speeds at Universal Studios Singapore, keeping track of football match scores, or managing their allowance for the newest gadgets, mastering algebra boosts their confidence in daily life. Our interactive lessons make learning fun and accessible. Because kids in Singapore learn in various ways, we customize our teaching to fit each child’s style. From bustling city streets to scenic gardens, BrightChamps makes math come alive throughout Singapore. Let’s make square roots an exciting part of every child’s math adventure!
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