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 fields such as architecture, engineering, and finance. Here, we will discuss the square root of 1145.
The square root is the inverse of the square of a number. 1145 is not a perfect square. The square root of 1145 is expressed in both radical and exponential forms. In radical form, it is expressed as √1145, whereas (1145)^(1/2) in the exponential form. √1145 ≈ 33.829, 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 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 1145 is broken down into its prime factors.
Step 1: Finding the prime factors of 1145 Breaking it down, we get 5 × 229: 5^1 × 229^1
Step 2: Now we found out the prime factors of 1145. Since 1145 is not a perfect square, the digits of the number can’t be grouped into pairs. Therefore, calculating 1145 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 numbers from right to left. In the case of 1145, we need to group it as 11 and 45.
Step 2: Now we need to find n whose square is less than or equal to 11. We can say n is 3 because 3 × 3 = 9 is less than 11. Now the quotient is 3, and after subtracting 9 from 11, the remainder is 2.
Step 3: Now let us bring down 45, which is the new dividend. Add the old divisor with the same number 3 + 3, we get 6, which will be our new divisor.
Step 4: The new divisor will be the sum of the dividend and quotient. Now we get 6n as the new divisor, and we need to find the value of n.
Step 5: The next step is finding 6n × n ≤ 245. Let us consider n as 4. Now 64 × 4 = 256 is greater than 245, so we try n as 3.
Step 6: With n = 3, 63 × 3 = 189. Subtract 245 from 189, and the difference is 56.
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. Now the new dividend is 5600.
Step 8: Now we need to find the new divisor, which is 669 because 669 × 8 = 5352.
Step 9: Subtracting 5352 from 5600, we get the result 248.
Step 10: Now the quotient is 33.8.
Step 11: Continue doing these steps until we get two numbers after the decimal point. Suppose if there are no decimal values, continue till the remainder is zero. So the square root of √1145 is approximately 33.82.
The approximation method is another approach 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 1145 using the approximation method.
Step 1: Now we have to find the closest perfect square to √1145. The smallest perfect square less than 1145 is 1089, and the largest perfect square greater than 1145 is 1225. √1145 falls somewhere between 33 and 34.
Step 2: Now we need to apply the formula that is (Given number - smallest perfect square) / (Greater perfect square - smallest perfect square). Using the formula (1145 - 1089) / (1225 - 1089) = 56 / 136 ≈ 0.4118. Using the formula, we identified the decimal point of our square root. The next step is adding the value we got initially to the decimal number, which is 33 + 0.4118 ≈ 33.82. So, the square root of 1145 is approximately 33.82.
Students can make mistakes while finding square roots, such as forgetting about the negative square root or skipping steps in long division methods. 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 √1145?
The area of the square is approximately 1145 square units.
The area of the square = side^2.
The side length is given as √1145.
Area of the square = side^2 = √1145 × √1145 = 1145.
Therefore, the area of the square box is approximately 1145 square units.
A square-shaped plot measuring 1145 square feet is to be divided in half; if each of the sides is √1145, what will be the square feet of half of the plot?
572.5 square feet
We can just divide the given area by 2 as the plot is square-shaped.
Dividing 1145 by 2 = 572.5
So half of the plot measures 572.5 square feet.
Calculate √1145 × 3.
Approximately 101.46
The first step is to find the square root of 1145, which is approximately 33.82.
The second step is to multiply 33.82 by 3.
So, 33.82 × 3 = 101.46
What will be the square root of (1145 + 55)?
The square root is 35.
To find the square root, we need to find the sum of (1145 + 55). 1145 + 55 = 1200, and then √1200 ≈ 34.64.
Therefore, the square root of (1145 + 55) is approximately 34.64.
Find the perimeter of a rectangle if its length 'l' is √1145 units and the width 'w' is 50 units.
The perimeter of the rectangle is approximately 217.64 units.
Perimeter of the rectangle = 2 × (length + width).
Perimeter = 2 × (√1145 + 50) ≈ 2 × (33.82 + 50) ≈ 2 × 83.82 ≈ 167.64 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.