119 LearnersLast updated on May 26th, 2025
Square Root of 617
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 617.
What is the Square Root of 617?
The square root is the inverse of the square of the number. 617 is not a perfect square. The square root of 617 is expressed in both radical and exponential form. In the radical form, it is expressed as √617, whereas (617)^(1/2) in the exponential form. √617 ≈ 24.81935, 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 617
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 617 by Prime Factorization Method
The product of prime factors is the prime factorization of a number. Now let us look at how 617 is broken down into its prime factors.
Step 1: Finding the prime factors of 617 617 is a prime number. Therefore, it cannot be broken down further into other prime factors.
Step 2: Since 617 is a prime number, it cannot be expressed as a product of smaller prime numbers. The prime factorization method cannot be used to simplify the square root of 617.
Square Root of 617 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 617, we need to group it as 17 and 6.
Step 2: Now we need to find n whose square is 6. We can say n as '2' because 2 x 2 = 4 is lesser than or equal to 6. Now the quotient is 2; after subtracting 6 - 4, the remainder is 2.
Step 3: Now let us bring down 17, which is the new dividend. Add the old divisor with the same number 2 + 2 we get 4, which will be our new divisor.
Step 4: The new divisor will be the sum of the dividend and quotient. Now we get 4n as the new divisor, we need to find the value of n.
Step 5: The next step is finding 4n × n ≤ 217. Let us consider n as 5, now 45 x 5 = 225, which is greater than 217. So, let's try n as 4. Now 44 x 4 = 176.
Step 6: Subtract 217 from 176; the difference is 41, and the quotient is 24.
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 zeros to the dividend. Now the new dividend is 4100.
Step 8: Now we need to find the new divisor that is 249 because 249 x 9 = 2241.
Step 9: Subtracting 2241 from 4100 we get the result 1859.
Step 10: Now the quotient is approximately 24.8.
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 √617 is approximately 24.819.
Square Root of 617 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 617 using the approximation method.
Step 1: Now we have to find the closest perfect square of √617. The smallest perfect square less than 617 is 576 and the largest perfect square greater than 617 is 625. √617 falls somewhere between 24 and 25.
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 (617 - 576) / (625 - 576) = 41 / 49 ≈ 0.8367. 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 24 + 0.8367 ≈ 24.8367, so the square root of 617 is approximately 24.8367.
Common Mistakes and How to Avoid Them in the Square Root of 617
Students do make mistakes while finding the square root, likewise 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 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. The correct way 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 617 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √617?
The area of the square is 617 square units.
Explanation
The area of the square = side².
The side length is given as √617.
Area of the square = side² = √617 x √617 = 617.
Therefore, the area of the square box is 617 square units.
Problem 2
A square-shaped building measuring 617 square feet is built; if each of the sides is √617, what will be the square feet of half of the building?
308.5 square feet
Explanation
We can just divide the given area by 2 as the building is square-shaped.
Dividing 617 by 2 = we get 308.5.
So half of the building measures 308.5 square feet.
Problem 3
Calculate √617 x 5.
124.09675
Explanation
The first step is to find the square root of 617, which is approximately 24.81935.
The second step is to multiply 24.81935 with 5.
So 24.81935 x 5 ≈ 124.09675.
Problem 4
What will be the square root of (617 + 8)?
The square root is approximately ±24.8395
Explanation
To find the square root, we need to find the sum of (617 + 8).
617 + 8 = 625, and then √625 = 25.
Therefore, the square root of (617 + 8) is ±25.
Problem 5
Find the perimeter of the rectangle if its length ‘l’ is √617 units and the width ‘w’ is 38 units.
We find the perimeter of the rectangle as approximately 125.6387 units.
Explanation
Perimeter of the rectangle = 2 × (length + width). Perimeter = 2 × (√617 + 38) = 2 × (24.81935 + 38) = 2 × 62.81935 ≈ 125.6387 units.
FAQ on Square Root of 617
1.What is √617 in its simplest form?
2.Mention the factors of 617.
3.Calculate the square of 617.
4.Is 617 a prime number?
5.617 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 617?
8.How do technology and digital tools in India support learning Algebra and Square Root of 617?
9.Does learning Algebra support future career opportunities for students in India?
Important Glossaries for the Square Root of 617
- Square root: A square root is the inverse of a square. Example: 4² = 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 natural number greater than 1 that cannot be formed by multiplying two smaller natural numbers.
- 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.
- Approximation method: A method used to estimate the value of a non-perfect square root by determining which two perfect squares it lies between and then finding a closer value through simple calculations.
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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
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