124 LearnersLast updated on May 26th, 2025
Square Root of 1529
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 like vehicle design, finance, etc. Here, we will discuss the square root of 1529.
What is the Square Root of 1529?
The square root is the inverse of the square of the number. 1529 is not a perfect square. The square root of 1529 is expressed in both radical and exponential form. In the radical form, it is expressed as √1529, whereas (1529)^(1/2) in the exponential form. √1529 ≈ 39.099, 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 1529
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 1529 by Prime Factorization Method
The product of prime factors is the prime factorization of a number. Now let us look at how 1529 is broken down into its prime factors.
Step 1: Finding the prime factors of 1529. Breaking it down, we get 1529 = 1 x 1529 (since 1529 is a prime number).
Step 2: Since 1529 is not a perfect square and it only has two factors, itself and 1, calculating 1529 using prime factorization is not applicable for finding the square root.
Square Root of 1529 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 1529, we can group it as 15 and 29.
Step 2: Now we need to find n whose square is less than or equal to 15. We can say n as ‘3’ because 3 x 3 = 9 is less than 15. Now the quotient is 3, and after subtracting 9 from 15, the remainder is 6.
Step 3: Bring down 29 to the right of the remainder, making it 629. 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 n such that 6n x n ≤ 629.
Step 5: Let us consider n as 9; then 69 x 9 = 621.
Step 6: Subtract 621 from 629; the difference is 8, and the quotient is 39.
Step 7: 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 800.
Step 8: The new divisor is 78, because 78 x 1 = 78, which is less than 800.
Step 9: Subtracting 78 from 800 gives us a remainder of 722.
Step 10: Now the quotient is 39.1
Step 11: Continue doing these steps until we get two numbers after the decimal point. Suppose if there are no decimal values, continue till the remainder is zero.
So the square root of √1529 is approximately 39.099.
Square Root of 1529 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 1529 using the approximation method.
Step 1: We have to find the closest perfect squares to √1529.
The smallest perfect square less than 1529 is 1521 (39^2) and the largest perfect square greater than 1529 is 1600 (40^2). √1529 falls somewhere between 39 and 40.
Step 2: Apply the formula (Given number - smallest perfect square) / (Greater perfect square - smallest perfect square). Using the formula (1529 - 1521) / (1600 - 1521) ≈ 0.101
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 39 + 0.101 ≈ 39.101.
Common Mistakes and How to Avoid Them in the Square Root of 1529
Students do make mistakes while finding the square root, such as 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 ≈ 7.071, there is also -7.071 which should not be forgotten.
Mistake 2
Not adding square root symbol in proper places
Not using the square root properly is another mistake that children make. To resolve this, we need to teach children that simplifying the numbers inside the square root is important and then move on to the second step.
For example: √(12+24) = √12 + √24 is the wrong method of using roots. The right way of using roots is √(12+24) = √36.
Mistake 3
Not finding the correct value of a non-perfect square
The first step that needs to be taught to children is to simplify the numbers inside the square root. This is important so that students do not make mistakes while identifying the approximate value.
For example: √50 ≈ 7 is wrong, the correct answer is √50 ≈ 7.071067.
Mistake 4
Confusing the square root symbol with the cube root
Students need to be taught the difference between cube root and square root constantly as this will help them avoid mistakes.
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, many students might skip a step accidentally, which results in a wrong answer at the end of the sum. This may either happen in subtracting or elsewhere.
Square root of 1529 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √140?
The area of the square is approximately 140 square units.
Explanation
The area of the square = side^2.
The side length is given as √140.
Area of the square = side^2 = √140 x √140 ≈ 11.832 x 11.832 ≈ 140.
Therefore, the area of the square box is approximately 140 square units.
Problem 2
A square-shaped building measuring 1529 square feet is built; if each of the sides is √1529, what will be the square feet of half of the building?
764.5 square meters
Explanation
We can just divide the given area by 2 as the building is square-shaped.
Dividing 1529 by 2 = we get 764.5
So half of the building measures 764.5 square meters.
Problem 3
Calculate √1529 x 5.
195.495
Explanation
The first step is to find the square root of 1529, which is approximately 39.099.
The second step is to multiply 39.099 by 5.
So 39.099 x 5 ≈ 195.495.
Problem 4
What will be the square root of (140 + 9)?
The square root is 13.
Explanation
To find the square root, we need to find the sum of (140 + 9). 140 + 9 = 149, which is not a perfect square, but the closest perfect square is 169 with a square root of 13.
Therefore, the square root of 149 is approximately 12.206.
Problem 5
Find the perimeter of the rectangle if its length ‘l’ is √140 units and the width ‘w’ is 38 units.
We find the perimeter of the rectangle as approximately 99.664 units.
Explanation
Perimeter of the rectangle = 2 × (length + width)
Perimeter = 2 × (√140 + 38) ≈ 2 × (11.832 + 38) ≈ 2 × 49.832 ≈ 99.664 units.
FAQ on Square Root of 1529
1.What is √1529 in its simplest form?
2.Mention the factors of 1529.
3.Calculate the square of 1529.
4.Is 1529 a prime number?
5.What is the decimal approximation of √1529?
6.How does learning Algebra help students in Singapore make better decisions in daily life?
7.How can cultural or local activities in Singapore support learning Algebra topics such as Square Root of 1529?
8.How do technology and digital tools in Singapore support learning Algebra and Square Root of 1529?
9.Does learning Algebra support future career opportunities for students in Singapore?
Important Glossaries for the Square Root of 1529
- 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: 1529 is a prime number.
- Perfect square: A perfect square is an integer that is the square of an integer. Example: 36 is a perfect square because it is 6^2.
- Decimal approximation: A decimal approximation is a numerical estimate of a number, which is not exact but close enough for practical purposes. Example: √1529 ≈ 39.099.
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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.
