104 LearnersLast updated on May 26th, 2025
Square Root of 2.01
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 engineering, finance, etc. Here, we will discuss the square root of 2.01.
What is the Square Root of 2.01?
The square root is the inverse of the square of the number. 2.01 is not a perfect square. The square root of 2.01 is expressed in both radical and exponential form. In the radical form, it is expressed as √2.01, whereas (2.01)^(1/2) in the exponential form. √2.01 ≈ 1.41774, 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 2.01
The prime factorization method is used for perfect square numbers. However, the prime factorization method is not applicable for non-perfect square numbers where long division method and approximation method are used. Let us now learn the following methods:
- Long division method
- Approximation method
Square Root of 2.01 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: Start by grouping the digits of 2.01 from right to left. The number can be grouped as 01 and 2.
Step 2: Find the largest integer whose square is less than or equal to 2. In this case, it is 1 since 1 * 1 = 1.
Step 3: Subtract 1 from 2, giving a remainder of 1. Bring down 01, making the new dividend 101.
Step 4: Double the divisor (which is 1) to get 2. Now find a digit n such that 2n * n is less than or equal to 101. Here, n is 4 because 24 * 4 = 96.
Step 5: Subtract 96 from 101 to get a remainder of 5.
Step 6: Since the dividend is less than the divisor, add a decimal point and bring down 00, making it 500.
Step 7: Double the current divisor (24) to get 48. Find n such that 48n * n is less than or equal to 500. Here, n is 1.
Step 8: Subtract 481 from 500 to get 19. Continue this process to find the next decimal places.
The square root of 2.01 is approximately 1.417.
Square Root of 2.01 by Approximation Method
The approximation method is another method for finding square roots, and 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 2.01 using the approximation method.
Step 1: Find the closest perfect squares around 2.01. The perfect square closest to 2 is 1, and the perfect square closest to 2.01 is 4. Thus, the square root of 2.01 lies between √1 and √4, which are 1 and 2, respectively.
Step 2: Use linear interpolation to approximate the square root. Let x be the approximate value of √2.01. Using the formula: x ≈ 1 + [(2.01 - 1) / (4 - 1)] * (2 - 1)
Step 3: Calculate: x ≈ 1 + (1.01 / 3) * 1 ≈ 1 + 0.3367 ≈ 1.3367 This is a rough approximation, but it shows the square root of 2.01 is approximately 1.41774.
Common Mistakes and How to Avoid Them in the Square Root of 2.01
Students do make mistakes while finding the square root, such as forgetting about the negative square root, skipping long division steps, 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 consider only the positive square root, as it is the required one.
For example, √2.01 ≈ 1.41774, but there is also -1.41774, which should not be forgotten.
Square Root of 2.01 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √2.01?
The area of the square is 2.01 square units.
Explanation
The area of the square = side².
The side length is given as √2.01.
Area of the square = side² = √2.01 × √2.01 = 2.01.
Therefore, the area of the square box is 2.01 square units.
Problem 2
A square-shaped building measuring 2.01 square feet is built; if each of the sides is √2.01, what will be the square feet of half of the building?
1.005 square feet
Explanation
We can just divide the given area by 2 as the building is square-shaped.
Dividing 2.01 by 2 = 1.005
So half of the building measures 1.005 square feet.
Problem 3
Calculate √2.01 × 5.
7.0887
Explanation
The first step is to find the square root of 2.01, which is approximately 1.41774.
The second step is to multiply 1.41774 by 5.
So, 1.41774 × 5 = 7.0887.
Problem 4
What will be the square root of (1.01 + 1)?
The square root is approximately 1.41774.
Explanation
To find the square root, we need to find the sum of (1.01 + 1).
1.01 + 1 = 2.01, and then √2.01 ≈ 1.41774.
Therefore, the square root of (1.01 + 1) is approximately ±1.41774.
Problem 5
Find the perimeter of the rectangle if its length ‘l’ is √2.01 units and the width ‘w’ is 3 units.
We find the perimeter of the rectangle as approximately 9.83548 units.
Explanation
Perimeter of the rectangle = 2 × (length + width)
Perimeter = 2 × (√2.01 + 3)
= 2 × (1.41774 + 3)
≈ 2 × 4.41774
≈ 8.83548 units.
FAQ on Square Root of 2.01
1.What is √2.01 in its simplest form?
2.Is 2.01 a perfect square?
3.Calculate the square of 2.01.
4.Is 2.01 a rational number?
5.What are the factors of 2.01?
6.How does learning Algebra help students in Qatar make better decisions in daily life?
7.How can cultural or local activities in Qatar support learning Algebra topics such as Square Root of 2.01?
8.How do technology and digital tools in Qatar support learning Algebra and Square Root of 2.01?
9.Does learning Algebra support future career opportunities for students in Qatar?
Important Glossaries for the Square Root of 2.01
- Square root: A square root is the inverse operation of squaring a number. For example, if 1.41^2 ≈ 2, then the square root of 2 is approximately 1.41.
- Irrational number: An irrational number is a number that cannot be written as a simple fraction. Its decimal form goes on forever without repeating.
- Rational number: A rational number can be expressed as the quotient or fraction of two integers.
- Perimeter: The perimeter is the total distance around the edge of a geometric figure.
- Decimal: A decimal is a fraction written in a special form. For example, instead of writing 1/2, you can express it as 0.5.
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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
: He loves to play the quiz with kids through algebra to make kids love it.
