126 LearnersLast updated on May 26th, 2025
Square Root of 1449
If a number is multiplied by itself, the result is a square. The inverse of squaring a number is finding its square root. The square root is used in various fields such as engineering, finance, etc. Here, we will discuss the square root of 1449.
What is the Square Root of 1449?
The square root is the inverse operation of squaring a number. 1449 is not a perfect square. The square root of 1449 is expressed in both radical and exponential form. In the radical form, it is expressed as √1449, whereas (1449)^(1/2) in exponential form. √1449 ≈ 38.048, 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 1449
The prime factorization method is used for perfect square numbers. However, for non-perfect square numbers, methods like 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 1449 by Prime Factorization Method
The product of prime factors is the prime factorization of a number. Now let us look at how 1449 is broken down into its prime factors.
Step 1: Finding the prime factors of 1449 Breaking it down, we get 3 x 3 x 7 x 23: 3^2 x 7 x 23
Step 2: We found the prime factors of 1449. The next step is to make pairs of those prime factors. Since 1449 is not a perfect square, grouping the digits into pairs is not possible.
Therefore, calculating √1449 using prime factorization is not straightforward.
Square Root of 1449 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, we need to group the numbers from right to left. In the case of 1449, we group it as 49 and 14.
Step 2: Now we need to find n whose square is less than or equal to 14. We can say n as '3' because 3 x 3 = 9, which is less than 14. The quotient is 3, and after subtracting 9 from 14, the remainder is 5.
Step 3: Bring down the next pair of digits, 49, making the new dividend 549. Add the old divisor with the same number: 3 + 3 = 6, which will be our new divisor.
Step 4: The new divisor will be 6n. We need to find the value of n.
Step 5: The next step is finding 6n x n ≤ 549. Let us consider n as 9; now 69 x 9 = 621.
Step 6: Since 621 is larger than 549, try n as 8. Then 68 x 8 = 544.
Step 7: The new remainder is 549 - 544 = 5.
Step 8: Since the dividend is less than the divisor, add a decimal point and bring down two zeroes. Now the new dividend is 500.
Step 9: Find the new divisor, which is 768 (68 concatenated with 8).
Step 10: Find the value of n such that 768n x n ≤ 500. Continue with this method until you reach the desired decimal places.
So the square root of √1449 is approximately 38.048.
Square Root of 1449 by Approximation Method
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 1449 using the approximation method.
Step 1: Find the closest perfect squares to √1449.
The smallest perfect square less than 1449 is 1225 (35^2) and the largest perfect square greater than 1449 is 1521 (39^2). √1449 falls somewhere between 35 and 39.
Step 2: Use linear approximation: (Given number - smallest perfect square) / (Greater perfect square - smallest perfect square). 1449 - 1225 = 224 and 1521 - 1225 = 296.
Using the formula, 224 ÷ 296 ≈ 0.757. Step 3: Adding this to the smaller perfect square root: 35 + 0.757 = 35.757, which is an approximation.
However, further refinement gives us 38.048 as a more accurate approximation.
Common Mistakes and How to Avoid Them in the Square Root of 1449
Students make mistakes while finding square roots, such as forgetting about the negative square root and skipping steps in the long division method. Let's look at a few common mistakes 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 usually take only the positive square root as it is the required one in most real-world situations.
For example, √50 = 7.071, but there is also -7.071, which should not be forgotten.
Mistake 2
Not adding the square root symbol in proper places
Not using the square root symbol properly is another mistake students make. To resolve this, students should be taught that simplifying numbers inside the square root is important before moving to the next step.
For example: √(12 + 24) = √36 is correct, while √12 + √24 is incorrect.
Mistake 3
Not finding the correct value of a non-perfect square
The first step that needs to be taught to students is to simplify the numbers inside the square root. This is important so that they do not make mistakes while identifying the approximate value.
For example: √50 ≈ 7.071067, not 7.
Mistake 4
Confusing the square root symbol with the cube root
Students need to be taught the difference between cube root and square root to avoid confusion.
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, students might skip a step accidentally, resulting in a wrong answer. This may happen during subtraction or elsewhere in the process.
Square Root of 1449 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √200?
The area of the square is 200 square units.
Explanation
The area of the square = side^2.
The side length is given as √200.
Area of the square = side^2 = √200 x √200 = 14.142 x 14.142 = 200
Therefore, the area of the square box is 200 square units.
Problem 2
A square-shaped garden measuring 1449 square feet is built; if each of the sides is √1449, what will be the square feet of half of the garden?
724.5 square feet
Explanation
We can just divide the given area by 2 as the garden is square-shaped.
Dividing 1449 by 2 gives us 724.5.
So half of the garden measures 724.5 square feet.
Problem 3
Calculate √1449 x 3.
114.144
Explanation
The first step is to find the square root of 1449, which is approximately 38.048.
The second step is to multiply 38.048 by 3.
So 38.048 x 3 = 114.144.
Problem 4
What will be the square root of (900 + 549)?
The square root is approximately 38.048.
Explanation
To find the square root, we need to sum (900 + 549). 900 + 549 = 1449, and then √1449 ≈ 38.048.
Therefore, the square root of (900 + 549) is approximately ±38.048.
Problem 5
Find the perimeter of the rectangle if its length ‘l’ is √200 units and the width ‘w’ is 50 units.
The perimeter of the rectangle is 128.284 units.
Explanation
Perimeter of the rectangle = 2 × (length + width).
Perimeter = 2 × (√200 + 50) = 2 × (14.142 + 50) = 2 × 64.142 = 128.284 units.
FAQ on Square Root of 1449
1.What is √1449 in its simplest form?
2.Mention the factors of 1449.
3.Calculate the square of 1449.
4.Is 1449 a prime number?
5.1449 is divisible by?
6.How does learning Algebra help students in Vietnam make better decisions in daily life?
7.How can cultural or local activities in Vietnam support learning Algebra topics such as Square Root of 1449?
8.How do technology and digital tools in Vietnam support learning Algebra and Square Root of 1449?
9.Does learning Algebra support future career opportunities for students in Vietnam?
Important Glossaries for the Square Root of 1449
- Square root: A square root is the inverse operation of squaring a number. For example, 6^2 = 36, and the inverse of squaring is finding the square root, √36 = 6.
- 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, but the positive square root is more commonly used in real-world applications. This is known as the principal square root.
- Approximation: The process of finding a value that is close to the exact solution, often used when dealing with non-perfect squares.
- Prime factorization: The process of expressing a number as the product of its prime factors, used to simplify calculations like finding square roots.
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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.
