118 LearnersLast updated on May 26th, 2025
Square Root of 1517
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 1517.
What is the Square Root of 1517?
The square root is the inverse of the square of a number. 1517 is not a perfect square. The square root of 1517 is expressed in both radical and exponential form. In radical form, it is expressed as √1517, whereas (1517)^(1/2) is the exponential form. √1517 ≈ 38.9504, 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 1517
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 and approximation methods are used. Let us now learn the following methods:
- Prime factorization method
- Long division method
- Approximation method
Square Root of 1517 by Prime Factorization Method
The product of prime factors is the prime factorization of a number. Now let us look at how 1517 is broken down into its prime factors.
Step 1: Finding the prime factors of 1517 Breaking it down, we get 1517 = 37 x 41.
Step 2: Now that we have found the prime factors of 1517, we realize that since 1517 is not a perfect square, the digits of the number can’t be grouped into pairs.
Therefore, calculating 1517 using prime factorization alone is not feasible.
Square Root of 1517 by Long Division Method
The long division method is particularly used for non-perfect square numbers. In this method, we check for the closest perfect square number to 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 1517, we group it as 15 and 17.
Step 2: Now, we need to find n whose square is less than or equal to 15. We can say n is ‘3’ because 3 x 3 = 9, which is less than 15. Now, the quotient is 3, and after subtracting 9 from 15, the remainder is 6.
Step 3: Now, let us bring down 17, making the new dividend 617. Add the old divisor with itself, 3 + 3, which gives us 6 as the new divisor.
Step 4: The new divisor will be 6n. We need to find the value of n such that 6n x n ≤ 617. Let us consider n as 9, then 69 x 9 = 621.
Step 5: Subtract 621 from 617, the difference is -4, but since this is incorrect, we adjust n to 8, so 68 x 8 = 544.
Step 6: Subtract 544 from 617, the difference is 73, and the quotient is 38.
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 7300.
Step 8: Now, we need to find the new divisor, which is 389, because 389 x 9 = 3501.
Step 9: Subtracting 3501 from 7300 gives the result 3799.
Step 10: Now, the quotient is 38.9.
Step 11: Continue these steps until we get two numbers after the decimal point. If there are no decimal values, continue until the remainder is zero.
So the square root of √1517 is approximately 38.95.
Square Root of 1517 by Approximation Method
The approximation method is another method for finding square roots, and 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 1517 using the approximation method.
Step 1: We have to find the closest perfect squares to √1517.
The smallest perfect square less than 1517 is 1521, and the largest perfect square close to 1517 is 1600. √1517 falls somewhere between 38 and 40.
Step 2: Now, we need to apply the formula: (Given number - smallest perfect square) / (Greater perfect square - smallest perfect square). Going by the formula (1517 - 1521) / (1600 - 1521) = -4 / 79 ≈ -0.0506.
Using the formula, we identified the adjustment to the nearest lower perfect square root. The next step is adjusting the value we got initially to the decimal number: 39 - 0.05 ≈ 38.95, so the square root of 1517 is approximately 38.95.
Common Mistakes and How to Avoid Them in the Square Root of 1517
Students do make mistakes while finding square roots, 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 = 7.07; there is also -7.07, which should not be forgotten.
Mistake 2
Not adding the 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 1517 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √1517?
The area of the square is 1517 square units.
Explanation
The area of the square = side^2.
The side length is given as √1517.
Area of the square = side^2 = √1517 x √1517 = 1517.
Therefore, the area of the square box is 1517 square units.
Problem 2
A square-shaped building measuring 1517 square feet is built; if each of the sides is √1517, what will be the square feet of half of the building?
758.5 square feet
Explanation
We can just divide the given area by 2 as the building is square-shaped.
Dividing 1517 by 2 = we get 758.5.
So half of the building measures 758.5 square feet.
Problem 3
Calculate √1517 x 5.
194.752
Explanation
The first step is to find the square root of 1517, which is approximately 38.95.
The second step is to multiply 38.95 by 5.
So 38.95 x 5 ≈ 194.752.
Problem 4
What will be the square root of (1517 + 9)?
The square root is 39.
Explanation
To find the square root, we need to find the sum of (1517 + 9). 1517 + 9 = 1526, and then √1526 ≈ 39.
Therefore, the square root of (1517 + 9) is approximately ±39.
Problem 5
Find the perimeter of the rectangle if its length ‘l’ is √1517 units and the width ‘w’ is 38 units.
We find the perimeter of the rectangle as 153.9 units.
Explanation
Perimeter of the rectangle = 2 × (length + width).
Perimeter = 2 × (√1517 + 38) = 2 × (38.95 + 38) ≈ 2 × 76.95 ≈ 153.9 units.
FAQ on Square Root of 1517
1.What is √1517 in its simplest form?
2.Mention the factors of 1517.
3.Calculate the square of 1517.
4.Is 1517 a prime number?
5.1517 is divisible by?
6.How does learning Algebra help students in Australia make better decisions in daily life?
7.How can cultural or local activities in Australia support learning Algebra topics such as Square Root of 1517?
8.How do technology and digital tools in Australia support learning Algebra and Square Root of 1517?
9.Does learning Algebra support future career opportunities for students in Australia?
Important Glossaries for the Square Root of 1517
- 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.
- Decimal: If a number has a whole number and a fraction in a single number, then it is called a decimal. For example: 7.86, 8.65, and 9.42 are decimals.
- Long division method: This method is used to find the square root of non-perfect squares by systematically dividing the number and finding its square root to several decimal places.
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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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