Last updated on May 26th, 2025
If a number is multiplied by the same number, the result is a square. The inverse of squaring a number is finding its square root. Square roots are used in fields such as vehicle design, finance, etc. Here, we will discuss the square root of 1445.
The square root is the inverse of the square of the number. 1445 is not a perfect square. The square root of 1445 is expressed in both radical and exponential form. In radical form, it is expressed as √1445, whereas in exponential form, it is (1445)^(1/2). √1445 ≈ 37.9987, 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 like 1445, 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 1445 is broken down into its prime factors.
Step 1: Finding the prime factors of 1445 Breaking it down, we get 5 x 17 x 17: 5^1 x 17^2
Step 2: Now we have found the prime factors of 1445. The second step is to make pairs of those prime factors. Since 1445 is not a perfect square, the digits of the number can’t be grouped in complete pairs.
Therefore, calculating 1445 using prime factorization alone isn't 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 1445, we need to group it as 45 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 is less than or equal to 14. Now the quotient is 3; after subtracting 9 from 14, the remainder is 5.
Step 3: Now let us bring down 45, which is the new dividend. Add the old divisor with the same number, 3 + 3, to get 6, which will be our new divisor.
Step 4: The new divisor will be the sum of the dividend and quotient. Now we have 6n as the new divisor, and we need to find the value of n.
Step 5: The next step is finding 6n × n ≤ 545. Let us consider n as 9, now 69 x 9 = 621.
Step 6: Subtract 545 from 621; the difference is negative, so we need to try n as 8. So, 68 x 8 = 544.
Step 7: Subtracting 544 from 545, the difference is 1, and the quotient is 38.
Step 8: Since the remainder is less than the divisor, add a decimal point. Adding the decimal point allows us to add two zeros to the dividend. Now the new dividend is 100.
Step 9: The new divisor is 760 because 760 x 1 = 760.
Step 10: Subtracting 760 from 1000, we get a result of 240.
Step 11: Continue these steps until we get two decimal places.
So the square root of √1445 ≈ 37.998
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 1445 using the approximation method.
Step 1: Now we have to find the closest perfect square of √1445.
The smallest perfect square less than 1445 is 1444, and the largest perfect square greater than 1445 is 1521. √1445 falls somewhere between 38 and 39.
Step 2: Now we need to apply the formula: (Given number - smallest perfect square)/(Next perfect square - smallest perfect square)
Using the formula (1445 - 1444) / (1521 - 1444) = 1/77 ≈ 0.01298 Adding this to the lower bound, we get 38 + 0.01298 = 38.01298.
So the square root of 1445 is approximately 38.01.
Students make mistakes while finding the square root, such as forgetting about the negative square root or skipping steps in the long division method. Now let us 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 √1445?
The area of the square is approximately 1445 square units.
The area of a square = side^2.
The side length is given as √1445.
Area of the square = side^2 = √1445 x √1445 = 1445.
Therefore, the area of the square box is approximately 1445 square units.
A square-shaped building measuring 1445 square feet is built; if each of the sides is √1445, what will be the square feet of half of the building?
722.5 square feet
We can just divide the given area by 2 as the building is square-shaped.
Dividing 1445 by 2 = 722.5.
So half of the building measures 722.5 square feet.
Calculate √1445 x 5.
189.994
The first step is to find the square root of 1445, which is approximately 37.9987.
The second step is to multiply 37.9987 by 5.
So 37.9987 x 5 = 189.994.
What will be the square root of (1445 + 100)?
The square root is approximately 40.25
To find the square root, we need to find the sum of (1445 + 100). 1445 + 100 = 1545, and then √1545 ≈ 40.25.
Therefore, the square root of (1445 + 100) is approximately ±40.25.
Find the perimeter of the rectangle if its length ‘l’ is √1445 units and the width ‘w’ is 38 units.
The perimeter of the rectangle is approximately 151.9974 units.
Perimeter of the rectangle = 2 × (length + width).
Perimeter = 2 × (√1445 + 38) = 2 × (37.9987 + 38) = 2 × 75.9987 = 151.9974 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.
: He loves to play the quiz with kids through algebra to make kids love it.