128 LearnersLast updated on May 26th, 2025
Square Root of 1520
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 1520.
What is the Square Root of 1520?
The square root is the inverse of the square of the number. 1520 is not a perfect square. The square root of 1520 is expressed in both radical and exponential form. In the radical form, it is expressed as √1520, whereas (1520)^(1/2) in the exponential form. √1520 ≈ 39.0128, 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 1520
The prime factorization method is used for perfect square numbers. However, the prime factorization method is not used for non-perfect square numbers where 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 1520 by Prime Factorization Method
The product of prime factors is the Prime factorization of a number. Now let us look at how 1520 is broken down into its prime factors:
Step 1: Finding the prime factors of 1520 Breaking it down, we get 2 x 2 x 2 x 2 x 5 x 19: 2^4 x 5^1 x 19^1
Step 2: Now we found out the prime factors of 1520. The second step is to make pairs of those prime factors. Since 1520 is not a perfect square, therefore the digits of the number can’t be grouped in pairs.
Therefore, calculating 1520 using prime factorization is not straightforward.
Square Root of 1520 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 1520, we can group it as 15 and 20.
Step 2: Now we need to find a number n whose square is less than or equal to 15. We can take 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: Now bring down the next pair of digits, 20, making the new dividend 620. The new divisor is 2 times the current quotient, which is 6.
Step 4: The next step is choosing a digit (let's call it x) such that 6x x x is less than or equal to 620. By trial, we find x = 9 works because 69 x 9 = 621, which is greater than 620, so we use x = 8 as 68 x 8 = 544.
Step 5: Subtract 544 from 620, and the remainder is 76. Add a decimal point and bring down a pair of zeros to make it 7600.
Step 6: The new divisor is 76, and we find a digit such that 768x x x is less than or equal to 7600. By trial, x = 9 works because 7689 x 9 = 6921.
Step 7: Subtract 6921 from 7600, and the remainder is 679. Continue this process to find more decimal places as needed.
So the square root of √1520 is approximately 39.0128.
Square Root of 1520 by Approximation Method
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 1520 using the approximation method.
Step 1: Now we have to find the closest perfect squares of √1520.
The smallest perfect square less than 1520 is 1444 (38^2) and the largest perfect square greater than 1520 is 1521 (39^2). √1520 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 (1520 - 1444) / (1521 - 1444) = 76 / 77 ≈ 0.987
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 + 0.987 = 38.987, so the square root of 1520 is approximately 39.0128.
Common Mistakes and How to Avoid Them in the Square Root of 1520
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 before moving on 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 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 ≈ 7.071, 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 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, resulting in a wrong answer at the end. This may either happen in subtracting or elsewhere.
Square Root of 1520 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √1520?
The area of the square is approximately 1520 square units.
Explanation
The area of the square = side^2.
The side length is given as √1520.
Area of the square = side^2 = √1520 x √1520 = 1520.
Therefore, the area of the square box is approximately 1520 square units.
Problem 2
A square-shaped building measuring 1520 square feet is built; if each of the sides is √1520, what will be the square feet of half of the building?
760 square feet
Explanation
We can just divide the given area by 2 as the building is square-shaped.
Dividing 1520 by 2 = we get 760.
So half of the building measures 760 square feet.
Problem 3
Calculate √1520 x 5.
195.064
Explanation
The first step is to find the square root of 1520, which is approximately 39.0128.
The second step is to multiply 39.0128 with 5.
So 39.0128 x 5 ≈ 195.064.
Problem 4
What will be the square root of (1500 + 20)?
The square root is approximately 39.0128.
Explanation
To find the square root, we need to find the sum of (1500 + 20) = 1520, and then √1520 ≈ 39.0128.
Therefore, the square root of (1500 + 20) is approximately ±39.0128.
Problem 5
Find the perimeter of the rectangle if its length ‘l’ is √1520 units and the width ‘w’ is 38 units.
The perimeter of the rectangle is approximately 154.0256 units.
Explanation
Perimeter of the rectangle = 2 × (length + width).
Perimeter = 2 × (√1520 + 38) ≈ 2 × (39.0128 + 38) ≈ 2 × 77.0128 ≈ 154.0256 units.
FAQ on Square Root of 1520
1.What is √1520 in its simplest form?
2.Mention the factors of 1520.
3.Calculate the square of 1520.
4.Is 1520 a prime number?
5.1520 is divisible by?
6.How does learning Algebra help students in India make better decisions in daily life?
7.How can cultural or local activities in India support learning Algebra topics such as Square Root of 1520?
8.How do technology and digital tools in India support learning Algebra and Square Root of 1520?
9.Does learning Algebra support future career opportunities for students in India?
Important Glossaries for the Square Root of 1520
- 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.
- Principal square root: A number has both positive and negative square roots; however, it is always the positive square root that has more prominence due to its uses in the real world. That is the reason it is also known as the principal square root.
- Prime factorization: The process of expressing a number as the product of prime numbers.
- Long division method: A step-by-step method used to divide two numbers and can also be used to find square roots of non-perfect squares.
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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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