BrightChamps Logo
Login
Creative Math Ideas Image
Live Math Learners Count Icon289 Learners

Last updated on May 26th, 2025

Math Whiteboard Illustration

Square root of 361

Professor Greenline Explaining Math Concepts

Square root is simply a number value that when multiplied with itself gives the original number. We apply square roots when we make financial estimations and solve practical problems in geometry.

Square root of 361 for Global Students
Professor Greenline from BrightChamps

What is the square root of 361?

The square root is the number that gives the original number when squared. 


√361 = 19,

 

in exponential form it is written as √361 =.3611/2 =19


In this article we will learn more about the square root of 361, how to find it and common mistakes one may make when trying to find the square root. 
 

Professor Greenline from BrightChamps

Finding the square root of 361


To find the square root of a number of students learn many methods. When a number is a perfect square and the process of finding square root is simple. 

Professor Greenline from BrightChamps

Square root using the prime factorization method

Breakdown 361 into prime factors, group them, and the result is the square root. 


Step 1: Prime factorize 


361 = 19×19


Step 2: Group factors in pairs


√361 = √19×19


Step 3: Multiply factors to find the square root


 √361 = 19
 

Professor Greenline from BrightChamps

Square root of 361 using the division method

Pair the digits, begin with the largest square and continue the subtraction and division till we find the result which is the square root of the number. 


Step 1: Pair 361


361 → (3)(61) 


Step 2: pick a number whose square is ≤ 3, 12=1


— 1 is the quotient. 


— Subtract the numbers, 3-1=2. 


— Bring down the numbers 61 next to the remainder, we get 261.


Step 3: double quotient and use it as the first digit of the new divisor’s


— Double 1


— Now find the digit x in a way that 2x×x ≤ 261 


— x is 9, 29×9 = 261.


Step 4: Now find the final quotient 


— The quotient we are left with 19, the square root of √361


The result; √361 = 19

Professor Greenline from BrightChamps

Square root of 361 using the repeated subtraction method

Subtract odd numbers that are consecutive, keep track of the number of subtractions until we reach 0. 


Step 1: Start the subtraction of consecutive odd numbers from 361, starting from 1. 


Step 2: Maintain a count of the number of the subtractions performed


361-1= 360


360-3 =357


357-5=352


352-7=345


Step 3: Continue the subtraction until the remainder is 0.


After performing 19 subtractions, the remainder is 0. The square root of the number is 19. 


The result; √361 = 19
 

Max Pointing Out Common Math Mistakes

Common mistakes and how to avoid them in square root of 361

Students make errors when learning to find the square root of a number. Here are errors and tips to avoid them. 
 

Mistake 1

Red Cross Icon Indicating Mistakes to Avoid in This Math Topic

Working individually on the numbers instead of working in pairs 
 

Green Checkmark Icon Indicating Correct Solutions in This Math Topic

When finding the square using the long division method, one may forget to work on pairs and not as individual numbers. 
 

Max from BrightChamps Saying "Hey"

Square root of 361 Examples

Ray, the Character from BrightChamps Explaining Math Concepts
Max, the Girl Character from BrightChamps

Problem 1

If x=√361 = solve x²+4x+5.

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

We know √361=19,

 

so x=19. Now substitute x into the expression:


x2+4x+5

 

=192+4(19)+5

 

=361+76+5

 

=442
 

Explanation

First, square x, then substitute into the equation to get the result.
 

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

Problem 2

Determine whether 361 is a prime or composite number using its square root.

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

The square root of 361 is ±19, meaning 361 is the square of 19. Since 19 is a prime number, and 361 has factors other than 1 and 361 (i.e.,19×19), 361 is a composite number.

Explanation

A composite number has more than two factors. Since 361 has a factorization involving 19, it is not a prime number.

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

Problem 3

Find the difference between the square roots of 400 and 361

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

 First, find the square roots of 400 and 361:


√400= 20 and √361=19 

 

Now find the difference:


20−19=1
 

Explanation

 The square roots of 400 and 361 are 20 and 19, respectively, and their difference is 1.
 

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

FAQs on the Square root of 361

1.Is 361 irrational?

Math FAQ Answers Dropdown Arrow

2.Is 361 a cube root?

Math FAQ Answers Dropdown Arrow

3.Is 5√7 irrational?

Math FAQ Answers Dropdown Arrow

4.What is the square root of 8?

Math FAQ Answers Dropdown Arrow

5.Is 2025 a perfect square?

Math FAQ Answers Dropdown Arrow
Professor Greenline from BrightChamps

Important glossaries for the square root of 361

  • Prime numbers — A number that has only two factors, 1 and the number itself. Prime numbers up to 10 are — 2,3,5,7.

 

  • Integer — A number between zero and infinite, that can be positive or negative, fraction or decimal. 

 

  • Perfect square number — a number whose square root has no decimal places in them. For example, the square root of 3600. 

 

  • Non-perfect square numbers — A number whose square has a fraction or decimal in its result. For example, square root of 117.
     
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