125 LearnersLast updated on May 26th, 2025
Square Root of 1185
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.
What is 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.
Finding the Square Root of 1185
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:
- Prime factorization method
- Long division method
- Approximation method
Square Root of 1185 by Prime Factorization Method
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.
Square Root of 1185 by Long Division Method
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.
Square Root of 1185 by Approximation Method
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.
Common Mistakes and How to Avoid Them in the Square Root of 1185
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.
Mistake 1
Forgetting about the negative square root
It is important to make students aware that a number has both positive and negative square roots. However, we usually only take the positive square root, as it is often the required one.
For example: √50 = 7.07, but there is also -7.07, which should not be forgotten.
Mistake 2
Not adding the square root symbol in proper places
Improper use of the square root symbol is another common mistake. To resolve this, we need to teach students that simplifying the numbers inside the square root is important before moving on to the next step.
For example: √(12 + 24) = √12 + √24 is incorrect. The correct usage is √(12 + 24) = √36.
Mistake 3
Not finding the correct value of a non-perfect square
The first step that needs to be taught to students is to simplify the numbers inside the square root. This is important so that students do not make mistakes while identifying the approximate value.
For example: √50 = 7 is incorrect; the correct answer is √50 ≈ 7.071.
Mistake 4
Confusing the square root symbol with the cube root
Students need to learn the difference between the cube root and the square root to avoid mistakes.
For example: √50 is different from ∛50.
Mistake 5
Making mistakes in long division
Finding a square root using the long division method involves many steps. Due to this, many students might accidentally skip a step, resulting in a wrong answer. This may occur during subtraction or elsewhere in the process.
Square root of 1185 Examples
Problem 1
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.
Explanation
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.
Problem 2
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.
Explanation
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.
Problem 3
Calculate √1185 x 5.
Approximately 172.2
Explanation
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.
Problem 4
What will be the square root of (1161 + 24)?
The square root is approximately 35.
Explanation
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.
Problem 5
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.
Explanation
Perimeter of the rectangle = 2 × (length + width)
Perimeter = 2 × (√1156 + 29)
= 2 × (34 + 29)
= 2 × 63
= 126 units.
FAQ on Square Root of 1185
1.What is √1185 in its simplest form?
2.Mention the factors of 1185.
3.Calculate the square of 1185.
4.Is 1185 a prime number?
5.1185 is divisible by?
6.How does learning Algebra help students in Canada make better decisions in daily life?
7.How can cultural or local activities in Canada support learning Algebra topics such as Square Root of 1185?
8.How do technology and digital tools in Canada support learning Algebra and Square Root of 1185?
9.Does learning Algebra support future career opportunities for students in Canada?
Important Glossaries for the Square Root of 1185
- Square root: A square root is the inverse of a square. Example: 4^2 = 16, and the inverse of the square is the square root, that is √16 = 4.
- Irrational number: An irrational number is a number that cannot be written as a simple fraction, meaning it cannot be expressed in the form of p/q, where q is not equal to zero, and p and q are integers.
- Principal square root: A number has both positive and negative square roots, but we often refer to the positive square root as the principal square root due to its practical applications in the real world.
- Prime factorization: The process of expressing a number as a product of its prime factors.
- Perfect square: A perfect square is an integer that is the square of another integer. For example, 16 is a perfect square because it is 4^2.
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Jaskaran Singh Saluja
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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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