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 =.361^1/2 =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
 

• 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.