Square root of 441

The square root is the number that gives the original number when it is multiplied twice. √441 = 21 in exponential form, it is written as √441 =441^1/2=21. In this article we will learn more about the square root of 441, how to find it and common mistakes.
 

Students learn different methods to find out square roots. For a perfect square root, the process is simple. Here, it is noticed that 441 is a perfect square. Few methods are explained below - 
 

Prime factorization of 441:

441 = 3×3×7×7 

For finding square roots, prime factorization is a usual way. In this method, a number is expressed as a product of prime factors. The number can be easily expressed as a whole number, as 441 is a rational number.
 

For the division method, the number has to be in pairs from the right side. Firstly, the number has to be segmented into pairs from the right side of the number. If there is an odd count of digits, then that digit has to be kept as it is.

The division method starts from the leftmost side of the number. The closest square number to the first segment can be used as a divisor. For this number, 41 has to be in pairs and 4 will be considered as a unit. As 22 = 4 therefore, the divisor will be 2 and the rest of the division it will follow.

Step 1: Pair 441

441 → (4)(41) 

Step 2: pick a number whose square is ≤ 4, 2²=4 

— 2 is the quotient. 

— Subtract the numbers, 4-4=0. 

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

— Double 2.

— Now find the digit x in a way that 4x×x = 41 

— x is 1, 41×1 = 41.

Step 4: Now find the final quotient 

— The quotient we are left with 21, the square root of √441

The result; √441 = 21
 

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 441, starting from 1. 

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

441-1= 440
440-3 =437
437-5=432
432-7=425

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

After performing 21 subtractions, the remainder is 0. The square root of the number is 21. 

The result; √441 = 21

• Integer — A number both positive and negative that lies between zero and infinity is called an integer.

• Prime numbers —  A number that can be divisible only by 1 or the number itself is called a prime number.

• Perfect square number — A number is called a perfect square when the root operation is applied, the answer comes out as a whole number.

• Non-perfect square numbers —  A number is called a non-perfect square number, if the root operation is applied, the answer comes out as a fraction.