117 LearnersLast updated on May 26th, 2025
Square Root of 577
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 577.
What is the Square Root of 577?
The square root is the inverse of the square of the number. 577 is not a perfect square. The square root of 577 is expressed in both radical and exponential form. In radical form, it is expressed as √577, whereas in exponential form it is expressed as (577)^(1/2). √577 ≈ 24.0208, 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 577
The prime factorization method is used for perfect square numbers. However, for non-perfect square numbers, the long division method and the approximation method are used. Let us now learn the following methods:
- Prime factorization method
- Long division method
- Approximation method
Square Root of 577 by Prime Factorization Method
The product of prime factors is the prime factorization of a number. Now let us look at how 577 is broken down into its prime factors:
Step 1: Finding the prime factors of 577 577 is a prime number, meaning it cannot be broken down further into smaller prime factors.
Therefore, prime factorization is not applicable here.
Square Root of 577 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 digits of 577 from right to left as 77 and 5.
Step 2: Now we need to find n whose square is closest to 5. We can say n as ‘2’ because 2 × 2 = 4 is less than or equal to 5. Now the quotient is 2, and after subtracting 4 from 5, the remainder is 1.
Step 3: Bring down 77, making the new dividend 177. Add the old divisor with the same number: 2 + 2 = 4, which will be our new divisor.
Step 4: Find n such that 4n × n ≤ 177. Let us consider n as 4. Now, 44 × 4 = 176.
Step 5: Subtract 176 from 177, the difference is 1, and the quotient is 24.
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 100.
Step 7: Find the new divisor 480 because 480 × 0 = 0.
Step 8: Subtract 0 from 100, and continue the process until you achieve the desired precision. The square root of √577 is approximately 24.0208.
Square Root of 577 by Approximation Method
The approximation method is another way to find 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 577 using the approximation method.
Step 1: Find the closest perfect squares around 577. The smallest perfect square before 577 is 576, and the next perfect square is 625. √577 falls between 24 and 25.
Step 2: Apply the formula: (Given number - smallest perfect square) / (Greater perfect square - smallest perfect square) Using the formula: (577 - 576) / (625 - 576) = 0.02
Step 3: Add the value obtained to the smaller square root: 24 + 0.02 = 24.02, so the square root of 577 is approximately 24.02.
Common Mistakes and How to Avoid Them in Finding the Square Root of 577
Students often make mistakes while finding square roots, such as forgetting about the negative square root or skipping steps in the long division method. Let us look at a few common mistakes in detail.
Mistake 1
Forgetting about the negative square root
It is important to remind students that a number has both positive and negative square roots. However, we typically focus on the positive square root, as it is generally required.
For example: √100 = 10, but there is also -10, which should not be forgotten.
Mistake 2
Not adding the square root symbol in proper places
Misplacing the square root symbol is another common mistake. Teach learners to simplify numbers inside the square root first before proceeding further.
For example: √(9 + 16) = √25 is correct, while writing it as √9 + √16 is incorrect.
Mistake 3
Not finding the correct value of a non-perfect square
The first step for students is to simplify numbers inside the square root. This prevents mistakes in identifying approximate values.
For example: √50 ≠ 7; the correct answer is √50 ≈ 7.071.
Mistake 4
Confusing the square root symbol with the cube root
Students need to learn the difference between cube roots and square roots to avoid confusion.
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, so students might skip a step accidentally, leading to wrong answers. This may occur during subtraction or elsewhere.
Square Root of 577 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √577?
The area of the square is 577 square units.
Explanation
The area of a square = side².
The side length is given as √577.
Area of the square = √577 × √577 = 577.
Therefore, the area of the square box is 577 square units.
Problem 2
A square-shaped building measuring 577 square feet is built; if each of the sides is √577, what will be the square feet of half of the building?
288.5 square feet
Explanation
We can divide the given area by 2 as the building is square-shaped.
Dividing 577 by 2 gives 288.5.
So half of the building measures 288.5 square feet.
Problem 3
Calculate √577 × 5.
120.104
Explanation
First, find the square root of 577, which is approximately 24.0208.
Multiply it by 5. So, 24.0208 × 5 ≈ 120.104.
Problem 4
What will be the square root of (576 + 1)?
The square root is approximately 24.0208.
Explanation
To find the square root, sum (576 + 1) = 577, then √577 ≈ 24.0208.
Therefore, the square root of (576 + 1) is approximately ±24.0208.
Problem 5
Find the perimeter of the rectangle if its length ‘l’ is √577 units and the width ‘w’ is 23 units.
The perimeter of the rectangle is approximately 94.0416 units.
Explanation
Perimeter of the rectangle = 2 × (length + width)
Perimeter = 2 × (√577 + 23) ≈ 2 × (24.0208 + 23) = 2 × 47.0208 ≈ 94.0416 units.
FAQ on Square Root of 577
1.What is √577 in its simplest form?
2.Mention the factors of 577.
3.Calculate the square of 577.
4.Is 577 a prime number?
5.577 is divisible by?
6.How does learning Algebra help students in United States make better decisions in daily life?
7.How can cultural or local activities in United States support learning Algebra topics such as Square Root of 577?
8.How do technology and digital tools in United States support learning Algebra and Square Root of 577?
9.Does learning Algebra support future career opportunities for students in United States?
Important Glossaries for the Square Root of 577
- Square root: The square root of a number is a value that, when multiplied by itself, gives the original number. Example: √16 = 4.
- Irrational number: An irrational number cannot be written as a simple fraction, i.e., in the form of p/q, where q is not equal to zero and p and q are integers.
- Prime number: A number greater than 1 that has no positive divisors other than 1 and itself. Example: 577.
- Long division method: A technique used to find the approximate square root of a number, especially for non-perfect squares.
- Decimal approximation: The process of finding an approximate decimal value for a square root that is not a perfect square.
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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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