101 LearnersLast updated on May 26th, 2025
Square Root of 1.41
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 1.41.
What is the Square Root of 1.41?
The square root is the inverse of squaring a number. 1.41 is not a perfect square. The square root of 1.41 is expressed in both radical and exponential form. In radical form, it is expressed as √1.41, whereas in exponential form it is expressed as (1.41)^(1/2). √1.41 ≈ 1.187, 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 1.41
The prime factorization method is used for perfect square numbers. However, for non-perfect square numbers, the long-division method and approximation method are used. Let us now learn the following methods:
- Long division method
- Approximation method
Square Root of 1.41 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 pair the numbers from right to left. For 1.41, we consider 1.41 as a single group.
Step 2: Determine the closest perfect square less than 1.41. The closest is 1, and its square root is 1.
Step 3: Subtract 1 from 1.41, giving 0.41. Bring down two zeros to make it 41.00.
Step 4: Double the previous quotient (1), making it 2. Now determine a digit (n) such that 2n*n ≤ 41.
Step 5: 2n needs to be the new divisor. Trying n=1 gives 21*1 = 21, which is less than 41.
Step 6: Subtract 21 from 41 to get 20. Bring down two more zeros, making it 2000.
Step 7: The process continues similarly until the desired precision is reached.
The square root of 1.41 is approximately 1.187.
Square Root of 1.41 by Approximation Method
The approximation method is another way to find square roots. It is an easy method for estimating the square root of a given number. Now let us learn how to find the square root of 1.41 using the approximation method.
Step 1: Identify the nearest perfect squares around 1.41. The closest are 1 (1^2) and 1.44 (1.2^2).
Step 2: Since 1.41 is closer to 1.44, we know √1.41 is closer to 1.2 but less than 1.2.
Step 3: Use interpolation: (1.41 - 1) / (1.44 - 1) = 0.41 / 0.44 ≈ 0.932
Step 4: Add this fraction to the smaller square root estimator: 1 + 0.932 * (1.2 - 1) = 1 + 0.932 * 0.2 = 1 + 0.1864 = 1.1864
Thus, the approximate square root of 1.41 is about 1.187.
Common Mistakes and How to Avoid Them in the Square Root of 1.41
Students often make mistakes while finding the square root, such as forgetting about the negative square root or skipping steps in the long division method. Let's look at a few of these mistakes in detail.
Mistake 1
Forgetting about the Negative Square Root
It's important to remember that every positive number has both positive and negative square roots. However, we typically refer to the principal (positive) square root.
For example, √1.41 ≈ ±1.187.
Square Root of 1.41 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √1.41?
The area of the square is approximately 1.407 square units.
Explanation
The area of the square = side².
The side length is given as √1.41.
Area of the square = side² = √1.41 × √1.41 ≈ 1.187 × 1.187 ≈ 1.407.
Therefore, the area of the square box is approximately 1.407 square units.
Problem 2
A square-shaped building measuring 1.41 square meters is built; if each of the sides is √1.41, what will be the square meters of half of the building?
0.705 square meters
Explanation
To find half of the building's area, simply divide the total area by 2.
Dividing 1.41 by 2 gives us 0.705.
So half the area of the building measures 0.705 square meters.
Problem 3
Calculate √1.41 × 5.
5.935
Explanation
First, find the approximate square root of 1.41, which is 1.187.
Then multiply by 5. So, 1.187 × 5 ≈ 5.935.
Problem 4
What will be the square root of (1.41 + 0.09)?
The square root is approximately 1.2
Explanation
To find the square root, first find the sum of (1.41 + 0.09).
1.41 + 0.09 = 1.50.
The approximate square root of 1.50 is 1.2.
Therefore, the square root of (1.41 + 0.09) is approximately ±1.2.
Problem 5
Find the perimeter of the rectangle if its length ‘l’ is √1.41 units and the width ‘w’ is 3 units.
The perimeter of the rectangle is approximately 8.374 units.
Explanation
Perimeter of the rectangle = 2 × (length + width).
Perimeter = 2 × (√1.41 + 3) ≈ 2 × (1.187 + 3) ≈ 2 × 4.187 = 8.374 units.
FAQ on Square Root of 1.41
1.What is √1.41 in its simplest form?
2.Mention the perfect squares closest to 1.41.
3.Calculate the square of 1.41.
4.Is 1.41 a prime number?
5.Is the square root of 1.41 rational or irrational?
6.How does learning Algebra help students in United Kingdom make better decisions in daily life?
7.How can cultural or local activities in United Kingdom support learning Algebra topics such as Square Root of 1.41?
8.How do technology and digital tools in United Kingdom support learning Algebra and Square Root of 1.41?
9.Does learning Algebra support future career opportunities for students in United Kingdom?
Important Glossary for the Square Root of 1.41
- Square root: A square root is the inverse of squaring a number. For example, 4^2 = 16, and the inverse is √16 = 4.
- Irrational number: An irrational number is a number that cannot be written as a simple fraction, where the denominator is not zero, and both numerator and denominator are integers.
- Principal square root: A number has both positive and negative square roots, but the positive square root is called the principal square root due to its common use.
- Decimal: A decimal is a number that includes a fractional part separated by a decimal point. For example, 7.86, 8.65, and 9.42 are decimals.
- Long division method: A manual arithmetic method used for calculating the square root of a number, particularly useful for non-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.
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