120 LearnersLast updated on May 26th, 2025
Square Root of 1066
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 various fields such as vehicle design, finance, etc. Here, we will discuss the square root of 1066.
What is the Square Root of 1066?
The square root is the inverse of the square of the number. 1066 is not a perfect square. The square root of 1066 is expressed in both radical and exponential form. In the radical form, it is expressed as √1066, whereas (1066)^(1/2) in the exponential form. √1066 ≈ 32.64965, 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 1066
The prime factorization method is used for perfect square numbers. However, the prime factorization method is not used for non-perfect square numbers where 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 1066 by Prime Factorization Method
The product of prime factors is the prime factorization of a number. Now let us look at how 1066 is broken down into its prime factors:
Step 1: Finding the prime factors of 1066. Breaking it down, we get 2 x 533: 2^1 x 533^1 (since 533 is a prime number).
Step 2: Now we found out the prime factors of 1066. The second step is to make pairs of those prime factors. Since 1066 is not a perfect square, the digits of the number can’t be grouped in pairs.
Therefore, calculating 1066 using prime factorization is impossible.
Square Root of 1066 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 1066, we need to group it as 66 and 10.
Step 2: Now we need to find n whose square is ≤ 10. We can say n as ‘3’ because 3 x 3 = 9, which is less 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 66, making the new dividend 166. 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 6n. We need to find the value of n.
Step 5: The next step is finding 6n x n ≤ 166. Let's consider n as 2, and 62 x 2 = 124.
Step 6: Subtract 124 from 166; the difference is 42, 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 4200.
Step 8: Now we need to find the new divisor, which is 649 because 649 x 6 = 3894.
Step 9: Subtracting 3894 from 4200, we get the result 306.
Step 10: Now the quotient is 32.6.
Step 11: Continue doing these steps until we get two numbers after the decimal point. Suppose if there is no decimal value, continue till the remainder is zero.
So, the square root of √1066 ≈ 32.65.
Square Root of 1066 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 1066 using the approximation method.
Step 1: Now we have to find the closest perfect square of √1066. The smallest perfect square less than 1066 is 1024, and the largest perfect square greater than 1066 is 1089. √1066 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). Using the formula, (1066 - 1024) ÷ (1089 - 1024) = 42 ÷ 65 ≈ 0.65. Using the formula, we identified the decimal point of our square root. The next step is adding the value we initially had to the decimal number, which is 32 + 0.65 = 32.65.
So the square root of 1066 is approximately 32.65.
Common Mistakes and How to Avoid Them in the Square Root of 1066
Students do make mistakes while finding the square root, like forgetting about the negative square root or skipping long division methods. 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, but there is also -7.07, which should not be forgotten.
Mistake 2
Not adding the 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, √(12+24) ≠ √12 + √24. The right way of using roots 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 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, √50 ≠ 7; the correct answer is √50 ≈ 7.071067.
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 avoid mistakes.
For example, √50 and ∛50 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 subtraction or elsewhere.
Square Root of 1066 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √1066?
The area of the square is approximately 1066 square units.
Explanation
The area of the square = side².
The side length is given as √1066.
Area of the square = side²
= √1066 x √1066
≈ 32.65 × 32.65
≈ 1066.
Therefore, the area of the square box is approximately 1066 square units.
Problem 2
A square-shaped building measuring 1066 square feet is built; if each of the sides is √1066, what will be the square feet of half of the building?
533 square feet
Explanation
We can just divide the given area by 2 as the building is square-shaped.
Dividing 1066 by 2, we get 533.
So half of the building measures 533 square feet.
Problem 3
Calculate √1066 x 5.
Approximately 163.25
Explanation
The first step is to find the square root of 1066, which is approximately 32.65.
The second step is to multiply 32.65 by 5.
So 32.65 x 5 ≈ 163.25.
Problem 4
What will be the square root of (1062 + 4)?
The square root is 33.
Explanation
To find the square root, we need to find the sum of (1062 + 4).
1062 + 4 = 1066, and then √1066 ≈ 32.65, rounded to the nearest whole number is 33.
Therefore, the square root of (1062 + 4) is approximately ±33.
Problem 5
Find the perimeter of the rectangle if its length ‘l’ is √1066 units and the width ‘w’ is 40 units.
We find the perimeter of the rectangle as approximately 145.3 units.
Explanation
Perimeter of the rectangle = 2 × (length + width).
Perimeter = 2 × (√1066 + 40)
≈ 2 × (32.65 + 40)
≈ 2 × 72.65
≈ 145.3 units.
FAQ on Square Root of 1066
1.What is √1066 in its simplest form?
2.Mention the factors of 1066.
3.Calculate the square of 1066.
4.Is 1066 a prime number?
5.1066 is divisible by?
6.How does learning Algebra help students in United States make better decisions in daily life?
7.How can cultural or local activities in United States support learning Algebra topics such as Square Root of 1066?
8.How do technology and digital tools in United States support learning Algebra and Square Root of 1066?
9.Does learning Algebra support future career opportunities for students in United States?
Important Glossaries for the Square Root of 1066
- Square root: A square root is the inverse of squaring a number. Example: 5² = 25, and the inverse of the square is the square root, which is √25 = 5.
- 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 is used in real-world applications. That is why it is also known as the principal square root.
- Prime number: A prime number is a natural number greater than 1 that cannot be formed by multiplying two smaller natural numbers. Example: 2, 3, 5, 7, etc.
- Decimal approximation: When a number cannot be expressed exactly, it is often rounded to a decimal for practical purposes. Example: √2 ≈ 1.414.
Explore More algebra
About BrightChamps in United States
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
: He loves to play the quiz with kids through algebra to make kids love it.
