272 LearnersLast updated on May 26th, 2025
Square root of 361
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.
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.
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.
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
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
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
Common mistakes and how to avoid them in square root of 361
Square root of 361 Examples
Problem 1
If x=√361 = solve x²+4x+5.
Explanation
Problem 2
Determine whether 361 is a prime or composite number using its square root.
Explanation
Problem 3
Find the difference between the square roots of 400 and 361
Explanation
FAQs on the Square root of 361
1.Is 361 irrational?
2.Is 361 a cube root?
3.Is 5√7 irrational?
4.What is the square root of 8?
5.Is 2025 a perfect square?
6.How does learning Algebra help students in Indonesia make better decisions in daily life?
7.How can cultural or local activities in Indonesia support learning Algebra topics such as Square root of 361 ?
8.How do technology and digital tools in Indonesia support learning Algebra and Square root of 361 ?
9.Does learning Algebra support future career opportunities for students in Indonesia?
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.
Explore More algebra
Previous to Square root of 361
About BrightChamps in Indonesia
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.
Fun Fact
: He loves to play the quiz with kids through algebra to make kids love it.
