102 LearnersLast updated on May 26th, 2025
Square Root of 1489
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 1489.
What is the Square Root of 1489?
The square root is the inverse of the square of a number. 1489 is not a perfect square. The square root of 1489 is expressed in both radical and exponential form. In the radical form, it is expressed as √1489, whereas (1489)^(1/2) in the exponential form. √1489 ≈ 38.588, 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 1489
The prime factorization method is used for perfect square numbers. However, the prime factorization method is not used for non-perfect square numbers where 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 1489 by Prime Factorization Method
The product of prime factors is the prime factorization of a number. Now let us look at how 1489 is broken down into its prime factors.
Step 1: Finding the prime factors of 1489 1489 is a prime number, so it cannot be broken down further into a product of smaller prime numbers. Since 1489 is not a perfect square, calculating its square root using prime factorization is impractical.
Square Root of 1489 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 1489, we need to group it as 14 and 89.
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. Now the quotient is 3, after subtracting 9 from 14, the remainder is 5.
Step 3: Now let us bring down 89, which is the new dividend. Add the old divisor with the same number, 3 + 3 = 6, which will be our new divisor.
Step 4: The new divisor will be the sum of the dividend and quotient. Now we get 6n as the new divisor. We need to find the value of n.
Step 5: The next step is finding 6n × n ≤ 589. Let us consider n as 9, now 69 x 9 = 621.
Step 6: Subtract 589 from 621, the difference is -32, which means n should be 8.
Step 7: The new divisor is 68. The result is 68 x 8 = 544.
Step 8: Subtracting 544 from 589 gives the remainder 45. The quotient is 38.
Step 9: Since the dividend is less than the divisor, we need to add a decimal point. Adding the decimal point allows us to add two zeroes to the dividend. Now the new dividend is 4500.
Step 10: Now we need to find the new divisor that is 386 because 386 x 1 = 386.
Step 11: Subtracting 386 from 4500 gives the result 4114. Step 12: Continue doing these steps until we achieve the desired precision.
The square root of √1489 is approximately 38.588.
Square Root of 1489 by Approximation Method
The 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 1489 using the approximation method.
Step 1: Now we have to find the closest perfect square of √1489.
The smallest perfect square less than 1489 is 1444 (38^2) and the largest perfect square more than 1489 is 1521 (39^2). √1489 falls somewhere between 38 and 39.
Step 2: Now we need to apply the formula that is (Given number - smallest perfect square) / (Greater perfect square - smallest perfect square). Going by the formula (1489 - 1444) / (1521 - 1444) = 0.54.
Using the formula, we identified the decimal point of our square root. The next step is adding the value we got initially to the decimal number which is 38 + 0.54 = 38.54, so the square root of 1489 is approximately 38.54.
Common Mistakes and How to Avoid Them in the Square Root of 1489
Students do make mistakes while finding the square root, like 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 does have both positive and negative square roots. However, we will be taking only the positive square root, as it is the required one.
For example: √50 ≈ 7.07, there is also -7.07 which should not be forgotten.
Square Root of 1489 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √1489?
The area of the square is approximately 2215.5841 square units.
Explanation
The area of the square = side^2.
The side length is given as √1489.
Area of the square = side^2 = √1489 x √1489 ≈ 38.588 x 38.588 ≈ 1489.
Therefore, the area of the square box is approximately 1489 square units.
Problem 2
A square-shaped building measuring 1489 square feet is built; if each of the sides is √1489, what will be the square feet of half of the building?
744.5 square feet
Explanation
We can just divide the given area by 2 as the building is square-shaped.
Dividing 1489 by 2 gives us 744.5.
So half of the building measures 744.5 square feet.
Problem 3
Calculate √1489 x 5.
192.94
Explanation
The first step is to find the square root of 1489, which is approximately 38.588.
The second step is to multiply 38.588 with 5.
So, 38.588 x 5 ≈ 192.94.
Problem 4
What will be the square root of (1444 + 45)?
The square root is 39.
Explanation
To find the square root, we need to find the sum of (1444 + 45). 1444 + 45 = 1489, and then √1489 ≈ 38.588.
Therefore, the square root of (1444 + 45) is approximately 39.
Problem 5
Find the perimeter of the rectangle if its length ‘l’ is √1489 units and the width ‘w’ is 50 units.
We find the perimeter of the rectangle as approximately 177.176 units.
Explanation
Perimeter of the rectangle = 2 × (length + width)
Perimeter = 2 × (√1489 + 50) ≈ 2 × (38.588 + 50) ≈ 2 × 88.588 ≈ 177.176 units.
FAQ on Square Root of 1489
1.What is √1489 in its simplest form?
2.Mention the factors of 1489.
3.Calculate the square of 1489.
4.Is 1489 a prime number?
5.1489 is divisible by?
6.How does learning Algebra help students in Canada make better decisions in daily life?
7.How can cultural or local activities in Canada support learning Algebra topics such as Square Root of 1489?
8.How do technology and digital tools in Canada support learning Algebra and Square Root of 1489?
9.Does learning Algebra support future career opportunities for students in Canada?
Important Glossaries for the Square Root of 1489
- Square root: A square root is the inverse of a square. Example: 4^2 = 16, and the inverse of the square is the square root, that is, √16 = 4.
- 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.
- Prime number: A prime number is a number that has exactly two distinct positive divisors: 1 and itself. Example: 2, 3, 5, 1489.
- Long division method: A technique used to find the square root of non-perfect squares by dividing the number into groups of digits and iteratively solving for decimal places.
- Decimal: A number that has a whole number and a fraction in a single number is called a decimal. Example: 7.86, 8.65, and 9.42 are decimals.
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Jaskaran Singh Saluja
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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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