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 the field of vehicle design, finance, etc. Here, we will discuss the square root of 1450.
The square root is the inverse of the square of the number. 1450 is not a perfect square. The square root of 1450 is expressed in both radical and exponential form. In the radical form, it is expressed as √1450, whereas in the exponential form it is (1450)^(1/2). √1450 ≈ 38.07887, 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, the prime factorization method is not used for non-perfect square numbers where the long-division method and approximation method are used. Let us now learn the following methods:
The product of prime factors is the prime factorization of a number. Now let us look at how 1450 is broken down into its prime factors.
Step 1: Finding the prime factors of 1450 Breaking it down, we get 2 x 5 x 5 x 29: 2^1 x 5^2 x 29^1
Step 2: Now we found out the prime factors of 1450. The second step is to make pairs of those prime factors. Since 1450 is not a perfect square, the digits of the number can’t be grouped into pairs.
Therefore, calculating 1450 using prime factorization is not straightforward.
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 numbers from right to left. In the case of 1450, we need to group it as 50 and 14.
Step 2: Now we need to find n whose square is less than or equal to 14. We can say n is ‘3’ because 3 x 3 = 9, which is less than 14. Now the quotient is 3, and after subtracting 9 from 14, the remainder is 5.
Step 3: Now let us bring down 50, which makes the new dividend 550. Add the old divisor with the same number, 3 + 3, we get 6 which will be part of our new divisor.
Step 4: The new divisor will be 6n. We need to find the value of n such that 6n x n ≤ 550. Let us consider n as 8; now 68 x 8 = 544.
Step 5: Subtract 544 from 550; the difference is 6, and the quotient is 38.
Step 6: 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. Now the new dividend is 600.
Step 7: Now we need to find the new divisor, which is 761 because 761 x 1 = 761 is larger than 600. Try with 760 x 0.
Step 8: Continue doing these steps until we get two numbers after the decimal point.
So the square root of √1450 ≈ 38.078.
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 1450 using the approximation method.
Step 1: Now we have to find the closest perfect square of √1450.
The smallest perfect square less than 1450 is 1444 (38^2), and the largest perfect square greater than 1450 is 1521 (39^2). √1450 falls somewhere between 38 and 39.
Step 2: Now we need to apply the formula: (Given number - smallest perfect square) / (Greater perfect square - smallest perfect square) Going by the formula (1450 - 1444) / (1521 - 1444) = 6/77 ≈ 0.078
Using the formula, we identified the decimal point for our square root. The next step is adding the value we got initially to the decimal number, which is 38 + 0.078 ≈ 38.078, so the square root of 1450 is approximately 38.078.
Students do make mistakes while finding the square root, such as forgetting about the negative square root or skipping long division steps. Now let us look at a few of those mistakes that students tend to make in detail.
Can you help Max find the area of a square box if its side length is given as √1450?
The area of the square is approximately 1450 square units.
The area of the square = side^2.
The side length is given as √1450.
The area of the square = side^2 = √1450 x √1450 = 1450.
Therefore, the area of the square box is approximately 1450 square units.
A square-shaped building measuring 1450 square feet is built; if each of the sides is √1450, what will be the square feet of half of the building?
725 square feet
We can divide the given area by 2 as the building is square-shaped.
Dividing 1450 by 2 = we get 725.
So half of the building measures 725 square feet.
Calculate √1450 x 5.
Approximately 190.39
The first step is to find the square root of 1450, which is approximately 38.078.
The second step is to multiply 38.078 by 5.
So 38.078 x 5 ≈ 190.39.
What will be the square root of (1450 + 50)?
The square root is approximately 40.
To find the square root, we need to find the sum of (1450 + 50). 1450 + 50 = 1500, and then √1500 ≈ 38.73.
Therefore, the square root of (1450 + 50) is approximately ±38.73.
Find the perimeter of the rectangle if its length ‘l’ is √1450 units and the width ‘w’ is 50 units.
We find the perimeter of the rectangle as approximately 176.16 units.
Perimeter of the rectangle = 2 × (length + width)
Perimeter = 2 × (√1450 + 50) = 2 × (38.078 + 50) = 2 × 88.078 ≈ 176.16 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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