121 LearnersLast updated on May 26th, 2025
Square Root of 524
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 524.
What is the Square Root of 524?
The square root is the inverse of the square of the number. 524 is not a perfect square. The square root of 524 is expressed in both radical and exponential form. In the radical form, it is expressed as √524, whereas (524)(1/2) in the exponential form. √524 ≈ 22.876, 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 524
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 524 by Prime Factorization Method
The product of prime factors is the prime factorization of a number. Now let us look at how 524 is broken down into its prime factors.
Step 1: Finding the prime factors of 524 Breaking it down, we get 2 x 2 x 131: 22 x 1311
Step 2: Now we found out the prime factors of 524. The second step is to make pairs of those prime factors. Since 524 is not a perfect square, the digits of the number can’t be grouped in pairs.
Therefore, calculating 524 using prime factorization is impossible.
Square Root of 524 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 524, we need to group it as 24 and 5.
Step 2: Now we need to find n whose square is 5. We can say n as ‘2’ because 2 x 2 is lesser than or equal to 5. Now the quotient is 2; after subtracting 4 (2 x 2) from 5, the remainder is 1.
Step 3: Now let us bring down 24, 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 current divisor and quotient. Now we get 4n as the new divisor, and we need to find the value of n.
Step 5: The next step is finding 4n x n ≤ 124. Let us consider n as 2; now 42 x 2 = 84.
Step 6: Subtract 124 from 84; the difference is 40, and the quotient is 22.
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 4000.
Step 8: Now we need to find the new divisor that is 229 because 229 x 9 = 2061.
Step 9: Subtracting 2061 from 4000, we get the result 1939.
Step 10: Now the quotient is 22.8.
Step 11: Continue doing these steps until we get two numbers after the decimal point. Suppose if there is no decimal value, continue till the remainder is zero.
So the square root of √524 is approximately 22.87.
Square Root of 524 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 524 using the approximation method.
Step 1: Now we have to find the closest perfect square of √524. The smallest perfect square of 524 is 484, and the largest perfect square of 524 is 529. √524 falls somewhere between 22 and 23.
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 (524 - 484) / (529 - 484) = 0.888.
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 22 + 0.888 ≈ 22.888, so the square root of 524 is approximately 22.888.
Common Mistakes and How to Avoid Them in the Square Root of 524
Students do make mistakes while finding the square root, like forgetting about the negative square root, skipping steps in 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.
Square Root of 524 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √524?
The area of the square is 524 square units.
Explanation
The area of the square = side2.
The side length is given as √524.
Area of the square = side2 = √524 x √524 = 524.
Therefore, the area of the square box is 524 square units.
Problem 2
A square-shaped building measuring 524 square feet is built; if each of the sides is √524, what will be the square feet of half of the building?
262 square feet
Explanation
We can just divide the given area by 2 as the building is square-shaped.
Dividing 524 by 2 = we get 262.
So half of the building measures 262 square feet.
Problem 3
Calculate √524 x 5.
114.38
Explanation
The first step is to find the square root of 524, which is approximately 22.876, and the second step is to multiply 22.876 with 5.
So 22.876 x 5 = 114.38.
Problem 4
What will be the square root of (500 + 24)?
The square root is 22.88
Explanation
To find the square root, we need to find the sum of (500 + 24).
500 + 24 = 524, and then √524 ≈ 22.88.
Therefore, the square root of (500 + 24) is approximately ±22.88.
Problem 5
Find the perimeter of the rectangle if its length ‘l’ is √524 units and the width ‘w’ is 38 units.
We find the perimeter of the rectangle as 123.752 units.
Explanation
Perimeter of the rectangle = 2 × (length + width)
Perimeter = 2 × (√524 + 38) ≈ 2 × (22.876 + 38) ≈ 2 × 60.876 ≈ 121.752 units.
FAQ on Square Root of 524
1.What is √524 in its simplest form?
2.Mention the factors of 524.
3.Calculate the square of 524.
4.Is 524 a prime number?
5.524 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 524?
8.How do technology and digital tools in United States support learning Algebra and Square Root of 524?
9.Does learning Algebra support future career opportunities for students in United States?
Important Glossaries for the Square Root of 524
- 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.
- Principal square root: A number has both positive and negative square roots; however, it is always a 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.
- Perfect square: A perfect square is a number that is the square of an integer. For example, 16 is a perfect square because it equals 42.
- Long division method: A mathematical technique used to find the square root of a non-perfect square by dividing the number into groups and solving step by step.
Explore More algebra
Previous to Square Root of 524
About BrightChamps in United States
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.
