102 LearnersLast updated on May 26th, 2025
Square Root of 1170
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 1170.
What is the Square Root of 1170?
The square root is the inverse of the square of a number. 1170 is not a perfect square. The square root of 1170 is expressed in both radical and exponential forms. In the radical form, it is expressed as √1170, whereas (1170)^(1/2) in the exponential form. √1170 ≈ 34.224, 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 1170
The prime factorization method is used for perfect square numbers. However, for non-perfect square numbers, 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 1170 by Prime Factorization Method
The product of prime factors is the prime factorization of a number. Now let us look at how 1170 is broken down into its prime factors:
Step 1: Finding the prime factors of 1170 Breaking it down, we get 2 x 3 x 3 x 5 x 13: 2^1 x 3^2 x 5^1 x 13^1
Step 2: Now we found out the prime factors of 1170. The second step is to make pairs of those prime factors. Since 1170 is not a perfect square, the digits of the number can’t be grouped in pairs. Therefore, calculating √1170 using prime factorization is not straightforward.
Square Root of 1170 by Long Division Method
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 1170, we need to group it as 70 and 11.
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 x 3 = 9, which 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 70, making the new dividend 270. Add the old divisor with the same number, 3 + 3 = 6, which will be our new divisor.
Step 4: We need to find a digit n such that 6n x n is less than or equal to 270. Let us consider n as 4, then 6 x 4 x 4 = 256.
Step 5: Subtract 256 from 270, the difference is 14, and the quotient is 34.
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 1400.
Step 7: Now we need to find the new divisor that is 688, because 688 x 2 = 1376.
Step 8: Subtracting 1376 from 1400 gives the result 24.
Step 9: Now the quotient is 34.2.
Step 10: Continue doing these steps until we get two numbers after the decimal point.
So the square root of √1170 is approximately 34.22.
Square Root of 1170 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 1170 using the approximation method.
Step 1: Now we have to find the closest perfect square of √1170. The smallest perfect square less than 1170 is 1156, and the largest perfect square greater than 1170 is 1225. √1170 falls somewhere between 34 and 35.
Step 2: Now we need to apply the formula: (Given number - smallest perfect square) / (Greatest perfect square - smallest perfect square). Using the formula: (1170 - 1156) ÷ (1225 - 1156) = 14 ÷ 69 ≈ 0.2029 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 34 + 0.2029 ≈ 34.2, so the square root of 1170 is approximately 34.2.
Common Mistakes and How to Avoid Them in the Square Root of 1170
Students do make mistakes while finding the square root, such as forgetting about the negative square root, skipping long division methods, etc. Now let us look at a few of those mistakes that 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 will be taking only the positive square root, as it is the required one.
For example: √50 = 7.07, there is also -7.07 which should not be forgotten.
Square Root of 1170 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √1170?
The area of the square is approximately 1367.376 square units.
Explanation
The area of the square = side^2.
The side length is given as √1170.
Area of the square = side^2 = √1170 x √1170 ≈ 34.224 x 34.224 ≈ 1367.376.
Therefore, the area of the square box is approximately 1367.376 square units.
Problem 2
A square-shaped building measuring 1170 square feet is built; if each of the sides is √1170, what will be the square feet of half of the building?
585 square feet
Explanation
We can just divide the given area by 2 as the building is square-shaped.
Dividing 1170 by 2, we get 585.
So half of the building measures 585 square feet.
Problem 3
Calculate √1170 x 5.
171.12
Explanation
The first step is to find the square root of 1170, which is approximately 34.224. The second step is to multiply 34.224 with 5. So 34.224 x 5 ≈ 171.12.
Problem 4
What will be the square root of (1156 + 14)?
The square root is 34.
Explanation
To find the square root, we need to find the sum of (1156 + 14). 1156 + 14 = 1170, and then √1170 ≈ 34.224. Therefore, the square root of (1156 + 14) is approximately ±34.224.
Problem 5
Find the perimeter of the rectangle if its length ‘l’ is √1170 units and the width ‘w’ is 30 units.
We find the perimeter of the rectangle as approximately 128.448 units.
Explanation
Perimeter of the rectangle = 2 × (length + width).
Perimeter = 2 × (√1170 + 30) ≈ 2 × (34.224 + 30) ≈ 2 × 64.224 ≈ 128.448 units.
FAQ on Square Root of 1170
1.What is √1170 in its simplest form?
2.Mention the factors of 1170.
3.Calculate the square of 1170.
4.Is 1170 a prime number?
5.1170 is divisible by?
6.How does learning Algebra help students in United Kingdom make better decisions in daily life?
7.How can cultural or local activities in United Kingdom support learning Algebra topics such as Square Root of 1170?
8.How do technology and digital tools in United Kingdom support learning Algebra and Square Root of 1170?
9.Does learning Algebra support future career opportunities for students in United Kingdom?
Important Glossaries for the Square Root of 1170
- Square root: The square root is the inverse of a square. For 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 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; however, it is always the positive square root that has more prominence due to its uses in the real world. That is the reason it is also known as the principal square root.
- Long division method: A systematic approach used to find the square root of a non-perfect square by dividing in a step-by-step manner.
- Approximation method: A method used to find the square root of a non-perfect square by estimating its value based on nearby perfect squares.
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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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