120 LearnersLast updated on May 26th, 2025
Square Root of 2017
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 2017.
What is the Square Root of 2017?
The square root is the inverse of the square of a number. 2017 is not a perfect square. The square root of 2017 is expressed in both radical and exponential form. In the radical form, it is expressed as √2017, whereas in exponential form it is (2017)^(1/2). √2017 ≈ 44.911, 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 2017
The prime factorization method is used for perfect square numbers. However, for non-perfect square numbers, the prime factorization method is not applicable, so we use the long-division method and approximation method. Let us now learn the following methods:
- Long division method
- Approximation method
Square Root of 2017 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 2017, group it as 20 and 17.
Step 2: Now, find n whose square is less than or equal to 20. We can say n as '4' because 4 × 4 = 16 is less than 20. The quotient is 4; after subtracting 16 from 20, the remainder is 4.
Step 3: Bring down 17 to make it 417. Add the old divisor (4) with the same number (4) to get 8, which will be our new divisor.
Step 4: The new divisor becomes 8n. We need to find the value of n such that 8n × n ≤ 417. Let us consider n as 5; now 85 × 5 = 425, which is more than 417. Try n as 4; 84 × 4 = 336.
Step 5: Subtract 336 from 417; the difference is 81. The quotient is 44.
Step 6: Since 81 is the remainder, we need to add a decimal point and continue the process. Add two zeroes to make it 8100.
Step 7: Now find the new divisor, which is 889, because 889 × 9 = 8001.
Step 8: Subtracting 8001 from 8100 gives us 99.
Step 9: Continue doing these steps until we get two numbers after the decimal point.
Thus, the square root of √2017 is approximately 44.91.
Square Root of 2017 by Approximation Method
The approximation method is another method for finding square roots, and it is an easy method for estimating the square root of a given number. Let us learn how to find the square root of 2017 using the approximation method.
Step 1: Find the closest perfect squares around √2017. The smallest perfect square less than 2017 is 1936 (44^2), and the largest perfect square greater than 2017 is 2025 (45^2). √2017 lies between 44 and 45.
Step 2: Apply the formula: (Given number - smallest perfect square) / (Greater perfect square - smallest perfect square). (2017 - 1936) / (2025 - 1936) = 81 / 89 ≈ 0.91 Adding this decimal to the lower bound gives 44 + 0.91 = 44.91, so the square root of 2017 is approximately 44.91.
Common Mistakes and How to Avoid Them in the Square Root of 2017
Students 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 typically consider 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 square root symbol in proper places
Not using the square root properly is another mistake that occurs. To resolve this, we teach that simplifying the numbers inside the square root is important before moving to the next step.
For example, √(12+24) = √12 + √24 is incorrect. The correct form is √(12+24) = √36.
Mistake 3
Not finding the correct value of a non-perfect square
The first step that needs to be taught is to simplify the numbers inside the square root. This is important so that students do not mistake identifying the approximate value.
For example, √50 ≠ 7; the correct answer is √50 ≈ 7.071.
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 to prevent 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, leading students to skip steps accidentally, resulting in wrong answers. This may happen during subtraction or elsewhere.
Square Root of 2017 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √1033?
The area of the square is approximately 1033 square units.
Explanation
The area of the square = side^2.
The side length is given as √1033.
Area = side^2 = √1033 × √1033 = 1033.
Therefore, the area of the square box is approximately 1033 square units.
Problem 2
A square-shaped building measuring 2017 square feet is built; if each of the sides is √2017, what will be the square feet of half of the building?
1008.5 square feet
Explanation
We can divide the given area by 2 as the building is square-shaped.
Dividing 2017 by 2 gives us 1008.5.
So, half of the building measures 1008.5 square feet.
Problem 3
Calculate √2017 × 5.
≈ 224.555
Explanation
The first step is to find the square root of 2017, which is approximately 44.911.
Then multiply 44.911 by 5.
So, 44.911 × 5 ≈ 224.555.
Problem 4
What will be the square root of (981 + 36)?
The square root is 33.
Explanation
To find the square root, we need to find the sum of (981 + 36). 981 + 36 = 1017. √1017 ≈ 31.87, approximately 32.
Therefore, the square root of (981 + 36) is approximately 32.
Problem 5
Find the perimeter of the rectangle if its length ‘l’ is √1033 units and the width ‘w’ is 25 units.
We find the perimeter of the rectangle as approximately 139.82 units.
Explanation
Perimeter of the rectangle = 2 × (length + width).
Perimeter = 2 × (√1033 + 25) ≈ 2 × (32.14 + 25) ≈ 2 × 57.14 ≈ 114.28 units.
FAQ on Square Root of 2017
1.What is √2017 in its simplest form?
2.Is 2017 a prime number?
3.Calculate the square of 2017.
4.What is the decimal approximation of √2017?
5.Is 2017 divisible by any smaller prime numbers?
6.How does learning Algebra help students in India make better decisions in daily life?
7.How can cultural or local activities in India support learning Algebra topics such as Square Root of 2017?
8.How do technology and digital tools in India support learning Algebra and Square Root of 2017?
9.Does learning Algebra support future career opportunities for students in India?
Important Glossaries for the Square Root of 2017
- Square root: A square root of a number is a value that, when multiplied by itself, gives the original number. For example, the square root of 16 is 4.
- Irrational number: An irrational number cannot be expressed as a fraction of two integers. Its decimal form is non-repeating and non-terminating.
- Prime number: A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself.
- Decimal approximation: A decimal approximation is an estimate of a number using decimal places to represent its value accurately.
- Long division method: A method used to find the square root of non-perfect squares by dividing the number and refining the result step by step.
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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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