Last updated on May 26th, 2025
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.
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.
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.
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
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
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
Students make errors when learning to find the square root of a number. Here are errors and tips to avoid them.
If x=√361 = solve x²+4x+5.
We know √361=19,
so x=19. Now substitute x into the expression:
x2+4x+5
=192+4(19)+5
=361+76+5
=442
First, square x, then substitute into the equation to get the result.
Determine whether 361 is a prime or composite number using its square root.
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.
A composite number has more than two factors. Since 361 has a factorization involving 19, it is not a prime number.
Find the difference between the square roots of 400 and 361
First, find the square roots of 400 and 361:
√400= 20 and √361=19
Now find the difference:
20−19=1
The square roots of 400 and 361 are 20 and 19, respectively, and their difference is 1.
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.
: He loves to play the quiz with kids through algebra to make kids love it.