124 LearnersLast updated on May 26th, 2025
Square Root of 453
If a number is multiplied by the same number, the result is a square. The inverse of the square is a square root. The square root is used in various fields such as vehicle design and finance. Here, we will discuss the square root of 453.
What is the Square Root of 453?
The square root is the inverse of the square of the number. 453 is not a perfect square. The square root of 453 can be expressed in both radical and exponential form. In the radical form, it is expressed as √453, whereas (453)^(1/2) in the exponential form. √453 ≈ 21.2838, which is an irrational number because it cannot be expressed in the form of p/q, where p and q are integers and q ≠ 0.
Finding the Square Root of 453
The prime factorization method is used for perfect square numbers. However, for non-perfect square numbers, methods like the long division method and approximation method are used. Let us now learn these methods:
- Prime factorization method
- Long division method
- Approximation method
Square Root of 453 by Prime Factorization Method
The product of prime factors is the prime factorization of a number. Now let us look at how 453 is broken down into its prime factors.
Step 1: Finding the prime factors of 453
Breaking it down, we get 3 x 151: 3^1 x 151^1
Step 2: Now we have found the prime factors of 453. The second step is to make pairs of those prime factors. Since 453 is not a perfect square, the digits of the number can’t be grouped in pairs.
Therefore, calculating 453 using prime factorization is not feasible.
Square Root of 453 by Long Division Method
The long division method is particularly used for non-perfect square numbers. In this method, we should check the closest perfect square number for the given number. Let us now learn how to find the square root using the long division method, step by step.
Step 1: To begin with, we need to group the digits from right to left. In the case of 453, we need to group it as 53 and 4.
Step 2: Now we need to find n whose square is less than or equal to 4. We can say n as ‘2’ because 2 x 2 = 4. Now the quotient is 2, and after subtracting 4 - 4, the remainder is 0.
Step 3: Now let us bring down 53, which is the new dividend. Add the old divisor with the same number: 2 + 2 = 4, which will be our new divisor.
Step 4: The new divisor will be 4n. We need to find the value of n such that 4n x n is less than or equal to 53.
Step 5: Let n be 1; now 41 x 1 = 41.
Step 6: Subtract 53 from 41, and the difference is 12. The quotient is now 21.
Step 7: Since the dividend is less than the divisor, we need to add a decimal point. Adding the decimal point allows us to add two zeroes to the dividend. The new dividend is 1200.
Step 8: Now we need to find the new divisor, which is 425 because 425 x 2 = 850.
Step 9: Subtracting 850 from 1200, we get 350.
Step 10: The quotient is now 21.2.
Step 11: Continue these steps until we get an accurate decimal value or until the remainder is zero.
The square root of √453 is approximately 21.283.
Square Root of 453 by Approximation Method
The approximation method is another method for finding square roots. It is an easy method to find the square root of a given number. Now let us learn how to find the square root of 453 using the approximation method.
Step 1: We have to find the closest perfect squares around √453. The smallest perfect square less than 453 is 441 (√441 = 21), and the smallest perfect square greater than 453 is 484 (√484 = 22). √453 falls somewhere between 21 and 22.
Step 2: Now we need to apply the formula: (Given number - smallest perfect square) / (Greater perfect square - smallest perfect square)
Using the formula (453 - 441) / (484 - 441) = 12 / 43 ≈ 0.279. Adding this to the lower perfect square root: 21 + 0.279 = 21.279, so the square root of 453 is approximately 21.279.
Common Mistakes and How to Avoid Them in the Square Root of 453
Students often make mistakes while finding square roots, such as forgetting about the negative square root or skipping steps in the long division method. Let's look at a few of these mistakes in detail.
Mistake 1
Forgetting about the negative square root
It is important to remind students that a number has both positive and negative square roots. However, we usually take only the positive square root, as it is the required one in most practical applications. For example, √50 = 7.07, and there is also -7.07, which should not be forgotten.
Mistake 2
Not adding the square root symbol in proper places
Misusing the square root symbol is another mistake that students make. It's important to simplify the numbers inside the square root first and then proceed.
For example, √(12+24) ≠ √12 + √24. The correct method is √(12+24) = √36.
Mistake 3
Not finding the correct value of a non-perfect square
The first step is to simplify the numbers inside the square root. This ensures students do not make mistakes while identifying the approximate value.
For example, √50 ≠ 7; the correct answer is √50 ≈ 7.071.
Mistake 4
Confusing the square root symbol with the cube root
Students need to be reminded frequently about the difference between cube roots and square roots to prevent confusion.
For example, √50 and ∛50 are different.
Mistake 5
Making mistakes in long division
Finding a square root using the long division method involves many steps. Due to this, students might accidentally skip a step, leading to a wrong answer. This may occur during subtraction or elsewhere.
Square Root of 453 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √453?
The area of the square is approximately 205.475 square units.
Explanation
The area of the square = side².
The side length is given as √453.
Area of the square = side² = √453 x √453 = 21.2838 x 21.2838 ≈ 205.475
Therefore, the area of the square box is approximately 205.475 square units.
Problem 2
A square-shaped building measuring 453 square feet is built. If each of the sides is √453, what will be the square feet of half of the building?
226.5 square feet
Explanation
We can divide the given area by 2, as the building is square-shaped.
Dividing 453 by 2, we get 226.5.
So, half of the building measures 226.5 square feet.
Problem 3
Calculate √453 x 5.
Approximately 106.42
Explanation
The first step is to find the square root of 453, which is approximately 21.2838.
The second step is to multiply 21.2838 by 5. 21.2838 x 5 ≈ 106.42
Problem 4
What will be the square root of (453 + 16)?
The square root is approximately 22.
Explanation
To find the square root, we need to find the sum of (453 + 16). 453 + 16 = 469, and √469 ≈ 21.66.
Therefore, the square root of (453 + 16) is approximately ±21.66.
Problem 5
Find the perimeter of the rectangle if its length ‘l’ is √453 units and the width ‘w’ is 53 units.
We find the perimeter of the rectangle as approximately 148.57 units.
Explanation
Perimeter of the rectangle = 2 × (length + width)
Perimeter = 2 × (√453 + 53) = 2 × (21.2838 + 53) = 2 × 74.2838 ≈ 148.57 units.
FAQ on Square Root of 453
1.What is √453 in its simplest form?
2.Mention the factors of 453.
3.Calculate the square of 453.
4.Is 453 a prime number?
5.453 is divisible by?
6.How does learning Algebra help students in Vietnam make better decisions in daily life?
7.How can cultural or local activities in Vietnam support learning Algebra topics such as Square Root of 453?
8.How do technology and digital tools in Vietnam support learning Algebra and Square Root of 453?
9.Does learning Algebra support future career opportunities for students in Vietnam?
Important Glossaries for the Square Root of 453
- Square root: A square root is the inverse of a square. Example: 4² = 16, and the inverse of the square is the square root that is √16 = 4.
- Irrational number: An irrational number is a number that cannot be written in the form of p/q, where q is not equal to zero and p and q are integers.
- Principal square root: A number has both positive and negative square roots; however, it is always the positive square root that has more prominence due to its uses in the real world. This is why it is also known as the principal square root.
- Prime factorization: The process of breaking down a number into its prime factors. For example, the prime factorization of 28 is 2 x 2 x 7.
- Long division method: A method used to find the square root of a number by dividing and finding the quotient over several steps, particularly useful for non-perfect squares.
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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.
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