100 LearnersLast updated on May 26th, 2025
Square Root of 1.49
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 the field of vehicle design, finance, etc. Here, we will discuss the square root of 1.49.
What is the Square Root of 1.49?
The square root is the inverse of the square of the number. 1.49 is not a perfect square. The square root of 1.49 is expressed in both radical and exponential form. In the radical form, it is expressed as √1.49, whereas (1.49)^(1/2) in the exponential form. √1.49 ≈ 1.22066, 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 1.49
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 1.49 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: Begin by grouping the digits from the decimal point. In the case of 1.49, it is already grouped as 1 and 49.
Step 2: Find the largest number whose square is less than or equal to 1. The number is 1 since 1 × 1 = 1. Now, the quotient is 1 and the remainder is 0.
Step 3: Bring down 49, making the new dividend 49. Add the previous divisor to itself, making it 2, which will be the new divisor.
Step 4: Find a number such that when it's placed next to 2 (making it 2n) and multiplied by n, the result is less than or equal to 49. Here, n is 2 because 22 × 2 = 44.
Step 5: Subtract 44 from 49, the remainder is 5.
Step 6: Add a decimal point in the quotient and bring down two zeros to make the remainder 500.
Step 7: Double the quotient obtained (12) to get 24 and find a number n such that 24n × n is less than or equal to 500. Here, n is 2 because 242 × 2 = 484.
Step 8: Subtract 484 from 500 to get the remainder 16.
Step 9: Continue this process to get a more accurate result. The quotient becomes 1.22 after two decimal places.
So, the square root of √1.49 is approximately 1.22.
Square Root of 1.49 by Approximation Method
The approximation method is another method for finding the 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 1.49 using the approximation method.
Step 1: Find the closest perfect squares around 1.49. The closest perfect squares are 1 (1^2) and 1.69 (1.3^2).
Step 2: Since 1.49 is closer to 1.69 than to 1, it follows that √1.49 is closer to 1.3. Using a linear approximation, we get: (Given number - smallest perfect square) / (Greater perfect square - smallest perfect square) (1.49 - 1) / (1.69 - 1) = 0.49 / 0.69 ≈ 0.71 Adding this approximation to the smaller integer, we get 1 + 0.71 = 1.71.
Thus, the approximate square root of 1.49 is 1.22.
Common Mistakes and How to Avoid Them in the Square Root of 1.49
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 us look at a few of these mistakes in detail.
Mistake 1
Forgetting about the Negative Square Root
It is important to remember that a number has both positive and negative square roots. However, we typically take only the principal (positive) square root.
For example: √1.49 ≈ 1.22, but there is also -1.22.
Square Root of 1.49 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √1.29?
The area of the square is approximately 1.6641 square units.
Explanation
The area of the square = side^2.
The side length is given as √1.29.
Area of the square = (√1.29)^2 = 1.29 ≈ 1.6641.
Therefore, the area of the square box is approximately 1.6641 square units.
Problem 2
A square-shaped plot measuring 1.49 square meters is built; if each of the sides is √1.49, what will be the square meters of half of the plot?
0.745 square meters
Explanation
The given area is 1.49 square meters.
To find half of the plot, divide the area by 2.
1.49 / 2 = 0.745.
So, half of the plot measures 0.745 square meters.
Problem 3
Calculate √1.49 x 3.
Approximately 3.66
Explanation
First, find the square root of 1.49, which is 1.22.
Then multiply 1.22 by 3. So, 1.22 x 3 ≈ 3.66.
Problem 4
What will be the square root of (0.49 + 1)?
The square root is 1.2
Explanation
To find the square root, first find the sum of (0.49 + 1).
0.49 + 1 = 1.49, and then √1.49 ≈ 1.22.
Therefore, the square root of (0.49 + 1) is approximately ±1.22.
Problem 5
Find the perimeter of the rectangle if its length ‘l’ is √1.69 units and the width ‘w’ is 0.8 units.
The perimeter of the rectangle is approximately 4.2 units.
Explanation
Perimeter of the rectangle = 2 × (length + width).
Perimeter = 2 × (√1.69 + 0.8)
= 2 × (1.3 + 0.8)
= 2 × 2.1
= 4.2 units.
FAQ on Square Root of 1.49
1.What is √1.49 in its simplest form?
2.How do you find the square root of 1.49?
3.Is 1.49 a perfect square?
4.What is the square of 1.49?
5.Is 1.49 a rational number?
6.How does learning Algebra help students in Oman make better decisions in daily life?
7.How can cultural or local activities in Oman support learning Algebra topics such as Square Root of 1.49?
8.How do technology and digital tools in Oman support learning Algebra and Square Root of 1.49?
9.Does learning Algebra support future career opportunities for students in Oman?
Important Glossaries for the Square Root of 1.49
- Square root: The square root is the inverse operation of squaring a number. Example: 3^2 = 9, and the square root of 9 is √9 = 3.
- Irrational number: An irrational number is a number that cannot be expressed as a simple fraction (p/q), where p and q are integers, and q ≠ 0.
- Principal square root: A number has both positive and negative square roots, but the principal square root refers to the positive root.
- Decimal: A decimal number is a number that includes a decimal point, representing a whole number and fractional part.
- Long division method: A step-by-step method used to find the square root of non-perfect squares by dividing and approximating the digits.
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About BrightChamps in Oman
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.
