Last updated on May 26th, 2025
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.
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.
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:
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.
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.
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.
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.
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.
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.
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
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.
Calculate √453 x 5.
Approximately 106.42
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
What will be the square root of (453 + 16)?
The square root is approximately 22.
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.
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.
Perimeter of the rectangle = 2 × (length + width)
Perimeter = 2 × (√453 + 53) = 2 × (21.2838 + 53) = 2 × 74.2838 ≈ 148.57 units.
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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