125 LearnersLast updated on May 26th, 2025
Square Root of 1071
If a number is multiplied by itself, 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 1071.
What is the Square Root of 1071?
The square root is the inverse of the square of a number. 1071 is not a perfect square. The square root of 1071 is expressed in both radical and exponential form. In the radical form, it is expressed as √1071, whereas (1071)^(1/2) in the exponential form. √1071 ≈ 32.718, 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 1071
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 1071 by Prime Factorization Method
The product of prime factors is the prime factorization of a number. Now let us look at how 1071 is broken down into its prime factors:
Step 1: Finding the prime factors of 1071 Breaking it down, we get 3 x 3 x 7 x 17: 3^2 x 7 x 17
Step 2: Now we found out the prime factors of 1071. The second step is to make pairs of those prime factors. Since 1071 is not a perfect square, the digits of the number can’t be grouped in pairs.
Therefore, calculating √1071 using prime factorization alone is not precise.
Square Root of 1071 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 1071, we need to group it as 71 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 less than 10. Now the quotient is 3 after subtracting 10 - 9, the remainder is 1.
Step 3: Bring down 71, making the new dividend 171. 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 previous divisor and a number. 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 ≤ 171. Let us consider n as 2, now 62 x 2 = 124.
Step 6: Subtract 171 from 124. The difference is 47, 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 4700.
Step 8: Now we need to find the new divisor. Trying 649 x 7 = 4543.
Step 9: Subtracting 4543 from 4700, we get the result 157.
Step 10: Now the quotient is 32.7.
Step 11: Continue doing these steps until we get two numbers after the decimal point. Suppose if there are no decimal values, continue till the remainder is zero.
So the square root of √1071 is approximately 32.718.
Square Root of 1071 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 1071 using the approximation method.
Step 1: Now we have to find the closest perfect squares of √1071. The smallest perfect square less than 1071 is 1024, and the largest perfect square greater than 1071 is 1089. √1071 falls somewhere between 32 and 33.
Step 2: Now we need to apply the formula that is (Given number - smallest perfect square) / (Greater perfect square - smallest perfect square). Using the formula (1071 - 1024) / (1089 - 1024) = 0.723. 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 + 0.723 = 32.723.
So the square root of 1071 is approximately 32.723.
Common Mistakes and How to Avoid Them in the Square Root of 1071
Students often make mistakes while finding square roots, such as forgetting about the negative square root, skipping long division steps, etc. Now let us look at a few of those 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 does have both positive and negative square roots. However, we usually take 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, resulting in a wrong answer at the end of the sum. This may either happen in subtracting or elsewhere.
Square Root of 1071 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √1071?
The area of the square is approximately 1071 square units.
Explanation
The area of the square = side².
The side length is given as √1071.
Area of the square = side²
= √1071 x √1071
= 1071.
Therefore, the area of the square box is approximately 1071 square units.
Problem 2
A square-shaped building measuring 1071 square feet is built; if each of the sides is √1071, what will be the square feet of half of the building?
Approximately 535.5 square feet.
Explanation
We can just divide the given area by 2 as the building is square-shaped.
Dividing 1071 by 2 = 535.5.
So half of the building measures approximately 535.5 square feet.
Problem 3
Calculate √1071 x 5.
Approximately 163.59.
Explanation
The first step is to find the square root of 1071, which is approximately 32.718.
The second step is to multiply 32.718 by 5.
So 32.718 x 5 ≈ 163.59.
Problem 4
What will be the square root of (1024 + 47)?
The square root is 33.
Explanation
To find the square root, we need to find the sum of (1024 + 47).
1024 + 47 = 1071, and then √1071 ≈ 32.718.
Therefore, the square root of (1024 + 47) is approximately 32.718.
Problem 5
Find the perimeter of the rectangle if its length ‘l’ is √1071 units and the width ‘w’ is 40 units.
The perimeter of the rectangle is approximately 145.436 units.
Explanation
Perimeter of the rectangle = 2 × (length + width).
Perimeter = 2 × (√1071 + 40)
= 2 × (32.718 + 40)
≈ 2 × 72.718
= 145.436 units.
FAQ on Square Root of 1071
1.What is √1071 in its simplest form?
2.Mention the factors of 1071.
3.Calculate the square of 1071.
4.Is 1071 a prime number?
5.1071 is divisible by?
6.How does learning Algebra help students in Thailand make better decisions in daily life?
7.How can cultural or local activities in Thailand support learning Algebra topics such as Square Root of 1071?
8.How do technology and digital tools in Thailand support learning Algebra and Square Root of 1071?
9.Does learning Algebra support future career opportunities for students in Thailand?
Important Glossaries for the Square Root of 1071
- Square root: A square root is the inverse of a square. For example: 4² = 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 used to find the square root of a non-perfect square number through successive approximations and divisions.
- Approximation method: A method used to estimate the square root of a number by comparing it to the nearest perfect squares.
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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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