118 LearnersLast updated on May 26th, 2025
Square Root of 1513
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 1513.
What is the Square Root of 1513?
The square root is the inverse of the square of the number. 1513 is not a perfect square. The square root of 1513 is expressed in both radical and exponential form. In the radical form, it is expressed as √1513, whereas (1513)^(1/2) is the exponential form. √1513 ≈ 38.898, 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 1513
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 1513 by Prime Factorization Method
The product of prime factors is the prime factorization of a number. Now let us look at how 1513 is broken down into its prime factors.
Step 1: Finding the prime factors of 1513 Breaking it down, we get 1513 = 37 x 41
Step 2: Now we found out the prime factors of 1513. Since 1513 is not a perfect square, the digits of the number can’t be grouped in pairs.
Therefore, calculating 1513 using prime factorization to find an exact square root is not feasible.
Square Root of 1513 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 1513, we need to group it as 13 and 15.
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, which is less than or equal to 15. The quotient is 3, and the remainder is 15 - 9 = 6.
Step 3: Bring down 13 to make the new dividend 613. Add the old divisor with the same number: 3 + 3 = 6, which will be our new divisor.
Step 4: Using 6n as the new divisor, find the value of n so that 6n x n is less than or equal to 613. Let us consider n as 9. Now, 69 x 9 = 621, which is greater than 613, so try n as 8, and 68 x 8 = 544.
Step 5: Subtract 544 from 613, the difference is 69, and the quotient is 38.
Step 6: Since the dividend is less than the divisor, add a decimal point. Adding the decimal point allows us to add two zeroes to the dividend, making it 6900.
Step 7: Find the new divisor 769 because 769 x 9 = 6921, which is greater than 6900. Try n as 8, and we get 768 x 8 = 6144.
Step 8: Subtract 6144 from 6900, which gives the result 756.
Step 9: Now the quotient is 38.8. Continue these steps until we obtain the desired decimal precision.
So the square root of √1513 ≈ 38.898.
Square Root of 1513 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. Let's learn how to find the square root of 1513 using the approximation method.
Step 1: Find the closest perfect squares around 1513.
The smallest perfect square less than 1513 is 1444 (38^2), and the largest perfect square more than 1513 is 1521 (39^2). √1513 falls between 38 and 39.
Step 2: Apply the formula: (Given number - smallest perfect square) / (Largest perfect square - smallest perfect square).
Using the formula: (1513 - 1444) / (1521 - 1444) ≈ 0.898. Add this to the smallest root: 38 + 0.898 ≈ 38.898, so the square root of 1513 is approximately 38.898.
Common Mistakes and How to Avoid Them in the Square Root of 1513
Students 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 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 often the required one.
For example: √50 ≈ 7.07, and there is also -7.07, which should not be forgotten.
Mistake 2
Not adding square root symbol in proper places
Not using the square root properly is another mistake. Teach students to simplify the numbers inside the square root first.
For example: √(12+24) = √36, not √12 + √24.
Mistake 3
Not finding the correct value of a non-perfect square
Simplify the numbers inside the square root first to avoid 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 reinforcement on the difference between cube roots and square roots.
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. Skipping a step accidentally can result in a wrong answer. This might happen in subtracting or other steps.
Square root of 1513 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √1513?
The area of the square is approximately 2291.29 square units.
Explanation
The area of a square = side^2.
The side length is given as √1513.
Area of the square = side^2 = √1513 x √1513 ≈ 38.898 x 38.898 ≈ 1513.
Therefore, the area of the square box is approximately 1513 square units.
Problem 2
A square-shaped building measuring 1513 square feet is built; if each of the sides is √1513, what will be the square feet of half of the building?
Approximately 756.5 square feet
Explanation
Divide the given area by 2 as the building is square-shaped.
Dividing 1513 by 2 gives approximately 756.5.
So half of the building measures approximately 756.5 square feet.
Problem 3
Calculate √1513 x 5.
Approximately 194.49
Explanation
The first step is to find the square root of 1513, which is approximately 38.898.
The second step is to multiply 38.898 by 5. So 38.898 x 5 ≈ 194.49.
Problem 4
What will be the square root of (1444 + 69)?
The square root is approximately 39.
Explanation
To find the square root, calculate (1444 + 69) = 1513. Then √1513 ≈ 38.898.
Therefore, the square root of (1444 + 69) is approximately ±39.
Problem 5
Find the perimeter of the rectangle if its length 'l' is √1513 units and the width 'w' is 50 units.
The perimeter of the rectangle is approximately 177.796 units.
Explanation
Perimeter of the rectangle = 2 × (length + width).
Perimeter = 2 × (√1513 + 50) = 2 × (38.898 + 50) ≈ 2 × 88.898 ≈ 177.796 units.
FAQ on Square Root of 1513
1.What is √1513 in its simplest form?
2.What are the factors of 1513?
3.Calculate the square of 1513.
4.Is 1513 a prime number?
5.1513 is divisible by?
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 1513?
8.How do technology and digital tools in Singapore support learning Algebra and Square Root of 1513?
9.Does learning Algebra support future career opportunities for students in Singapore?
Important Glossaries for the Square Root of 1513
- Square root: A square root is the inverse of a square. For example, 4^2 = 16, and the inverse of the square is the square root, which 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 usually the positive square root that is used in practical applications. This is known as the principal square root.
- Prime factorization: Prime factorization is the process of expressing a number as the product of its prime factors.
- Decimal number: A decimal number contains a whole number and a fractional part separated by a decimal point, e.g., 38.898.
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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.
