124 LearnersLast updated on May 26th, 2025
Square Root of 1065
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 like vehicle design, finance, etc. Here, we will discuss the square root of 1065.
What is the Square Root of 1065?
The square root is the inverse of the square of the number. 1065 is not a perfect square. The square root of 1065 is expressed in both radical and exponential form. In the radical form, it is expressed as √1065, whereas (1065)^(1/2) in the exponential form. √1065 ≈ 32.619, 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 1065
The prime factorization method is used for perfect square numbers. However, for non-perfect square numbers, the prime factorization method is not used; 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 1065 by Prime Factorization Method
The product of prime factors is the prime factorization of a number. Now let us look at how 1065 is broken down into its prime factors.
Step 1: Finding the prime factors of 1065 Breaking it down, we get 3 x 5 x 71: 3^1 x 5^1 x 71^1
Step 2: Now we found the prime factors of 1065. The second step is to make pairs of those prime factors. Since 1065 is not a perfect square, the digits of the number can’t be grouped into pairs.
Therefore, calculating 1065 using prime factorization is not straightforward.
Square Root of 1065 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 1065, we need to group it as 65 and 10.
Step 2: Now we need to find n whose square is less than or equal to 10. We can say n is ‘3’ because 3 x 3 = 9, which is lesser than or equal to 10. Now the quotient is 3, and after subtracting 9 from 10, the remainder is 1.
Step 3: Now let us bring down 65, 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; we need to find the value of n.
Step 5: The next step is finding 6n x n ≤ 165. Let us consider n as 2; now 62 x 2 = 124.
Step 6: Subtract 165 from 124; the difference is 41, and the quotient is 32.
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 4100.
Step 8: Now we need to find the new divisor that is 649 because 649 x 6 = 3894.
Step 9: Subtracting 3894 from 4100, we get the result 206.
Step 10: Now the quotient is 32.6.
Step 11: Continue doing these steps until we get two numbers after the decimal point. Suppose there is no decimal value; continue until the remainder is zero.
So the square root of √1065 is approximately 32.62.
Square Root of 1065 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 1065 using the approximation method.
Step 1: Now we have to find the closest perfect square of √1065. The smallest perfect square less than 1065 is 1024, and the largest perfect square greater than 1065 is 1089. √1065 falls somewhere between 32 and 33.
Step 2: Now we need to apply the formula: (Given number - smallest perfect square) / (Greater perfect square - smallest perfect square) Going by the formula (1065 - 1024) / (1089 - 1024) = 41 / 65 ≈ 0.63. 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 32 + 0.63 = 32.63.
So the square root of 1065 is approximately 32.63.
Common Mistakes and How to Avoid Them in the Square Root of 1065
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 does have both positive and negative square roots. However, we will be taking only the positive square root, as it is the required one.
For example, √1065 ≈ 32.62; there is also -32.62, which should not be forgotten.
Mistake 2
Not adding square root symbol in proper places
Not using the square root properly is another mistake that children make. To resolve this, we need to teach children that simplifying the numbers inside the square root is important and then move on to the second step.
For example, √(32+33) = √32 + √33 is a wrong method of using roots. The right way of using roots is √(32+33) = √65.
Mistake 3
Not finding the correct value of a non-perfect square
The first step that needs to be taught to children 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, √65 ≈ 8.06, not 8.
Mistake 4
Confusing the square root symbol with the cube root
Students need to be taught the difference between cube root and square root constantly, as this will help them keep away from mistakes.
For example, √1065 and ∛1065 are different.
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 skip a step accidentally, which results in a wrong answer at the end of the sum. This may either happen in subtracting or elsewhere.
Square Root of 1065 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √1065?
The area of the square is approximately 1065 square units.
Explanation
The area of the square = side^2.
The side length is given as √1065.
Area of the square = side^2
= √1065 x √1065
= 1065.
Therefore, the area of the square box is approximately 1065 square units.
Problem 2
A square-shaped building measuring 1065 square feet is built; if each of the sides is √1065, what will be the square feet of half of the building?
532.5 square feet
Explanation
We can just divide the given area by 2 as the building is square-shaped.
Dividing 1065 by 2, we get 532.5.
So half of the building measures 532.5 square feet.
Problem 3
Calculate √1065 x 5.
Approximately 163.095
Explanation
The first step is to find the square root of 1065, which is approximately 32.619, the second step is to multiply 32.619 by 5. So, 32.619 x 5 ≈ 163.095.
Problem 4
What will be the square root of (1000 + 65)?
The square root is approximately 32.619.
Explanation
To find the square root, we need to find the sum of (1000 + 65).
1000 + 65 = 1065, and then √1065 ≈ 32.619.
Therefore, the square root of (1000 + 65) is approximately ±32.619.
Problem 5
Find the perimeter of the rectangle if its length ‘l’ is √1065 units and the width ‘w’ is 20 units.
We find the perimeter of the rectangle as approximately 105.238 units.
Explanation
Perimeter of the rectangle = 2 × (length + width).
Perimeter = 2 × (√1065 + 20)
= 2 × (32.619 + 20)
= 2 × 52.619
≈ 105.238 units.
FAQ on Square Root of 1065
1.What is √1065 in its simplest form?
2.Mention the factors of 1065.
3.Calculate the square of 1065.
4.Is 1065 a prime number?
5.1065 is divisible by?
6.How does learning Algebra help students in United Arab Emirates make better decisions in daily life?
7.How can cultural or local activities in United Arab Emirates support learning Algebra topics such as Square Root of 1065?
8.How do technology and digital tools in United Arab Emirates support learning Algebra and Square Root of 1065?
9.Does learning Algebra support future career opportunities for students in United Arab Emirates?
Important Glossaries for the Square Root of 1065
- 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, which 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 method of dividing large numbers to find a quotient, often used to find the square root of non-perfect squares.
- Approximation method: A method used to find an approximate value of a square root by identifying perfect squares around the given number.
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Jaskaran Singh Saluja
About the Author
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.
Fun Fact
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