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 vehicle design, finance, etc. Here, we will discuss the square root of 1185.
The square root is the inverse of the square of a number. 1185 is not a perfect square. The square root of 1185 is expressed in both radical and exponential form. In radical form, it is expressed as √1185, whereas (1185)^(1/2) in exponential form. √1185 ≈ 34.435, 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.
For perfect square numbers, the prime factorization method is used. However, for non-perfect square numbers, the prime factorization method is not applicable, and instead, 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 1185 is broken down into its prime factors:
Step 1: Finding the prime factors of 1185 Breaking it down, we get 3 x 5 x 79.
Step 2: Now we found out the prime factors of 1185. The second step is to make pairs of those prime factors. Since 1185 is not a perfect square, the digits of the number can't be grouped in pairs.
Therefore, calculating √1185 using prime factorization is not feasible.
The long division method is particularly used for non-perfect square numbers. In this method, we find the closest perfect square number to 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 1185, we need to group it as 11 and 85.
Step 2: Now we need to find n whose square is less than or equal to 11. We can say n as '3' because 3 x 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 85, which is the new dividend. Add the old divisor with the same number 3 + 3, which gives us 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, where we need to find the value of n.
Step 5: The next step is finding 6n x n ≤ 285. Let's consider n as 4, hence 64 x 4 = 256.
Step 6: Subtract 256 from 285, the difference is 29, and the quotient becomes 34.
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 2900.
Step 8: Now we need to find the new divisor. Let's consider n as 4, so 688 x 4 = 2752.
Step 9: Subtract 2752 from 2900, we get the result 148.
Step 10: Now the quotient is 34.4.
Step 11: Continue these steps until we get two numbers after the decimal point. If there are no decimal values, continue until the remainder is zero.
So the square root of √1185 ≈ 34.44.
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 1185 using the approximation method.
Step 1: Now, we have to find the closest perfect square to √1185. The smallest perfect square less than 1185 is 1156 (34^2), and the largest perfect square greater than 1185 is 1225 (35^2). √1185 falls somewhere between 34 and 35.
Step 2: Now we need to asing the formula (1185 - 1156) / (1225 - 1156) = 29/69 ≈ 0.42 pply the formula: (Given number - smallest perfect square) / (Greater perfect square - smallest perfect square) UUsing the formula, we identified the decimal point of our square root. The next step is adding the initial integer value to the decimal number, which is 34 + 0.42 = 34.42, so the square root of 1185 is approximately 34.42.
Students often make mistakes while finding the square root, such as forgetting about the negative square root or skipping steps in the long division method. Let's look at some common mistakes students tend to make in detail.
Can you help Max find the area of a square box if its side length is given as √1255?
The area of the square is approximately 1255 square units.
The area of the square = side^2.
The side length is given as √1255.
Area of the square = side^2 = √1255 x √1255 ≈ 35.43 x 35.43 ≈ 1255.
Therefore, the area of the square box is approximately 1255 square units.
A square-shaped building measuring 1185 square feet is built; if each of the sides is √1185, what will be the square feet of half of the building?
Approximately 592.5 square feet.
We can just divide the given area by 2 as the building is square-shaped.
Dividing 1185 by 2 gives us approximately 592.5.
So, half of the building measures approximately 592.5 square feet.
Calculate √1185 x 5.
Approximately 172.2
The first step is to find the square root of 1185, which is approximately 34.44.
The second step is to multiply 34.44 by 5.
So 34.44 x 5 ≈ 172.2.
What will be the square root of (1161 + 24)?
The square root is approximately 35.
To find the square root, we need to find the sum of (1161 + 24).
1161 + 24 = 1185, and then √1185 ≈ 34.44.
Therefore, the square root of (1161 + 24) is approximately ±34.44.
Find the perimeter of the rectangle if its length ‘l’ is √1156 units and the width ‘w’ is 29 units.
The perimeter of the rectangle is 126 units.
Perimeter of the rectangle = 2 × (length + width)
Perimeter = 2 × (√1156 + 29)
= 2 × (34 + 29)
= 2 × 63
= 126 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.