115 LearnersLast updated on May 26th, 2025
Square Root of 1417
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 1417.
What is the Square Root of 1417?
The square root is the inverse of the square of a number. 1417 is not a perfect square. The square root of 1417 can be expressed in both radical and exponential forms. In radical form, it is expressed as √1417, whereas in exponential form, it is written as (1417)^(1/2). √1417 ≈ 37.645, 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 1417
The prime factorization method is used for perfect square numbers. However, the prime factorization method is not suitable 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 1417 by Prime Factorization Method
The product of prime factors is the prime factorization of a number. Now let us look at how 1417 is broken down into its prime factors:
Step 1: Finding the prime factors of 1417 Breaking it down, we find it is already a product of prime numbers: 1417 is 1417 x 1, as 1417 is a prime number.
Step 2: Since 1417 is a prime number and not a perfect square, calculating 1417 using prime factorization is not feasible for finding its square root.
Square Root of 1417 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 numbers 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 1417, we can group it as 17 and 14.
Step 2: Now we need to find n whose square is less than or equal to 14. We can say n is 3 because 3 x 3 = 9, which is less than 14. Now the quotient is 3, and after subtracting 9 from 14, the remainder is 5.
Step 3: Now let us bring down 17, making the new dividend 517. Add the old divisor (3) with itself to get 6, which will be part of our new divisor.
Step 4: The new divisor will be 6n, where n is a digit such that 6n x n is less than or equal to 517. Let us try n = 8, then 68 x 8 = 544, which is too large. Try n = 7, then 67 x 7 = 469, which is less than 517.
Step 5: Subtract 469 from 517, and the remainder is 48. The quotient is now 37.
Step 6: Since the remainder is not zero, add a decimal point to the quotient, and bring down two zeros to make the new dividend 4800.
Step 7: The new divisor is 674 (67 doubled plus 4), and we find a new digit n such that 674n x n is less than or equal to 4800. Let n be 7, then 6747 x 7 = 4729.
Step 8: Subtract 4729 from 4800, the remainder is 71, and the quotient is 37.7.
Step 9: Continue doing these steps until we get two digits after the decimal point.
The square root of √1417 is approximately 37.65.
Square Root of 1417 by Approximation Method
The approximation method is another approach 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 1417 using the approximation method.
Step 1: Now we have to find the closest perfect square of √1417.
The smallest perfect square less than 1417 is 1369 (37^2), and the largest perfect square greater than 1417 is 1444 (38^2). √1417 falls somewhere between 37 and 38.
Step 2: Now we need to apply the formula: (Given number - smallest perfect square) / (Greater perfect square - smallest perfect square).
Using the formula: (1417 - 1369) / (1444 - 1369) = 48 / 75 ≈ 0.64. Adding this value to 37 gives us 37 + 0.64 = 37.64, so the square root of 1417 is approximately 37.64.
Common Mistakes and How to Avoid Them in the Square Root of 1417
Students often make mistakes while finding the square root, such as forgetting about the negative square root, skipping long division steps, 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 has both positive and negative square roots. However, we usually consider only the positive square root, as it is the required one.
For example: √50 = 7.07, but 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 next step.
For Example: √(12+24) = √12 + √24 is incorrect. The correct method 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, resulting in a wrong answer at the end of the calculation. This may happen in subtracting or elsewhere.
Square Root of 1417 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √1417?
The area of the square is 1417 square units.
Explanation
The area of the square = side².
The side length is given as √1417.
Area of the square = side² = √1417 x √1417 = 1417.
Therefore, the area of the square box is 1417 square units.
Problem 2
A square-shaped building measuring 1417 square feet is built. If each of the sides is √1417, what will be the square feet of half of the building?
708.5 square feet
Explanation
We can divide the given area by 2 as the building is square-shaped.
Dividing 1417 by 2 gives us 708.5.
So half of the building measures 708.5 square feet.
Problem 3
Calculate √1417 x 5.
188.225
Explanation
The first step is to find the square root of 1417, which is approximately 37.645.
The second step is to multiply 37.645 by 5.
So 37.645 x 5 = 188.225.
Problem 4
What will be the square root of (1417 + 6)?
The square root is approximately 38.
Explanation
To find the square root, we need to find the sum of (1417 + 6). 1417 + 6 = 1423.
Approximating √1423, which is close to 38, as 38^2 = 1444.
Therefore, the square root of (1417 + 6) is approximately ±38.
Problem 5
Find the perimeter of the rectangle if its length ‘l’ is √1417 units and the width ‘w’ is 38 units.
The perimeter of the rectangle is approximately 151.29 units.
Explanation
Perimeter of the rectangle = 2 × (length + width).
Perimeter = 2 × (√1417 + 38) ≈ 2 × (37.645 + 38) ≈ 2 × 75.645 = 151.29 units.
FAQ on Square Root of 1417
1.What is √1417 in its simplest form?
2.Is 1417 a prime number?
3.Calculate the square of 1417.
4.What are the factors of 1417?
5.Is 1417 divisible by any smaller numbers?
6.How does learning Algebra help students in United Kingdom make better decisions in daily life?
7.How can cultural or local activities in United Kingdom support learning Algebra topics such as Square Root of 1417?
8.How do technology and digital tools in United Kingdom support learning Algebra and Square Root of 1417?
9.Does learning Algebra support future career opportunities for students in United Kingdom?
Important Glossaries for the Square Root of 1417
- Square root: A square root is the inverse of a square. For example, 4² = 16 and the inverse of the square is the square root, which is √16 = 4.
- Prime number: A number greater than 1 that has no positive divisors other than 1 and itself. Example: 2, 3, 5, 7, etc.
- 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.
- Long division method: A technique used to find square roots of non-perfect squares involving a series of steps of division and subtraction.
- Approximation: A method for finding a close value to the actual quantity, often used when an exact value is difficult to obtain.
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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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