349 LearnersLast updated on May 26th, 2025
Square root of 441
Square root is a mathematical operation where a factor of a number is multiplied by itself, giving the original number. For financial estimations, geometry problems, the function of square root is used. In this topic, we will learn about the square root of 441.
What is the 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 =4411/2=21. In this article we will learn more about the square root of 441, how to find it and common mistakes.
Finding the square root of 441
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 -
Square Root of 441 By Prime Factorization
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.
Square Root of 441 By Long division
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
Square Root of 441 By Approximation
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
Common Mistakes and How to Avoid Them in the Square Root of 441
Children learn square root in grade 6 or 7. It is quite usual to make mistakes while solving square root. Few mistakes are explained below
Mistake 1
Working individually on the numbers instead of working in pairs
When finding the square using the long division method, one may forget to work on pairs and not as individual numbers.
Mistake 2
Getting confused between square root and squaring
The square, 4412 is, 194481 and the square root, √441 is 21. Children sometimes may make mistakes in applying the operation.
Mistake 3
Making mistakes in the repeated subtraction method
Any order of the numbers cannot be subtracted, this leads to inconsistencies to find the square root of the number. Make a note to just subtract consecutive odd numbers that start as 1,3,5,7 and so on.
Square root of 441 Examples
Problem 1
Find the Value of 2×√441+5/3
√441=21
Now substitute the value of √441 into the expression:
2×21+5/3=42+5/3=47/3=15.67
Explanation
find the square root of 441 and then we follow the order of operations (multiplication first, followed by addition and division) to simplify the expression.
Problem 2
If the area of a square is 441 cm², find the perimeter of the square.
The area of a square is → A=s2, s is the side length.
To find the side length:
s=√441=21cm
The perimeter P of a square is 4×s
P=4×21=84
Explanation
We use the square root of the area to find the side length of the square, and then calculate the perimeter by multiplying the side length by 4.
Problem 3
Solve for x in the equation 5x²=2205
First, divide both sides by 5:
x2=2205/5=441
Square both the sides:
x=±√441=±21
Explanation
We first isolate x2 by dividing by 5, then take the square root of both sides. Since square roots can be positive or negative, we get two possible solutions, x=21 or x=−21x.
Problem 4
Evaluate √441/√49
√441=21 and √49=7
Now divide:
21/7=3
Explanation
We first find the square roots of both 441 and 49, then divide the results to get the final answer.
FAQs on the Square root of 441
1.Is 441 a perfect square?
2.What is the factorization of 441?
3. Is 441 divisible by 441?
4. What are the factors of 441?
5.Is √441 rational?
6.How does learning Algebra help students in United States make better decisions in daily life?
7.How can cultural or local activities in United States support learning Algebra topics such as Square root of 441 ?
8.How do technology and digital tools in United States support learning Algebra and Square root of 441 ?
9.Does learning Algebra support future career opportunities for students in United States?
Important glossaries for the square root of 441
- 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.
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