122 LearnersLast updated on May 26th, 2025
Square Root of 5300
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 5300.
What is the Square Root of 5300?
The square root is the inverse of the square of the number. 5300 is not a perfect square. The square root of 5300 is expressed in both radical and exponential form. In radical form, it is expressed as √5300, whereas (5300)^(1/2) in exponential form. √5300 ≈ 72.8011, 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 5300
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 5300 by Prime Factorization Method
The product of prime factors is the prime factorization of a number. Now let us look at how 5300 is broken down into its prime factors.
Step 1: Finding the prime factors of 5300
Breaking it down, we get 2 x 2 x 5 x 5 x 53: 2^2 x 5^2 x 53
Step 2: Now we have found out the prime factors of 5300. The second step is to make pairs of those prime factors. Since 5300 is not a perfect square, the digits of the number can’t be completely grouped in pairs. Therefore, calculating √5300 using prime factorization gives an approximate value.
Square Root of 5300 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 5300, we need to group it as 00 and 53.
Step 2: Now we need to find n whose square is less than or equal to 53. We can say n is ‘7’ because 7 x 7 = 49, which is less than 53. The quotient is 7, and after subtracting 49 from 53, the remainder is 4.
Step 3: Now let us bring down 00, making the new dividend 400. Add 7 (the last digit of the quotient) to the divisor, making it 14.
Step 4: The new divisor will be 14n. We need to find the value of n such that 14n x n ≤ 400. Let us consider n as 2, so 142 x 2 = 284.
Step 5: Subtracting 284 from 400, the difference is 116.
Step 6: 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 11600.
Step 7: Now we need to find the new divisor, which is 145 (since 142 + 3 = 145) because 145 x 8 = 1160.
Step 8: Subtracting 1160 from 11600 gives us 0.
Step 9: The quotient is 72.8.
Step 10: Continue doing these steps until we get two numbers after the decimal point. Suppose there are no decimal values; continue till the remainder is zero.
So the square root of √5300 is approximately 72.80.
Square Root of 5300 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 5300 using the approximation method.
Step 1: Now we have to find the closest perfect squares of √5300. The smallest perfect square less than 5300 is 4900, and the largest perfect square greater than 5300 is 5625. √5300 falls somewhere between 70 and 75.
Step 2: Now we need to apply the formula: (Given number - smallest perfect square)/(Greater perfect square - smallest perfect square). Using the formula, (5300 - 4900)/(5625 - 4900) = 400/725 ≈ 0.552. 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 70 + 0.552 = 70.552, so the square root of 5300 is approximately 72.80.
Common Mistakes and How to Avoid Them in the Square Root of 5300
Students do make mistakes while finding the square root, 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 usually take only the principal (positive) square root for practical applications.
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 symbol properly is another mistake that students make. To resolve this, we need to teach students 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 way is √(12 + 24) = √36 = 6.
Mistake 3
Not finding the correct value of a non-perfect square
The first step that needs to be taught to students 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 incorrect; the correct answer is √50 ≈ 7.071.
Mistake 4
Confusing the square root symbol with the cube root
Students need to be taught the difference between cube roots and square roots 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 occur during subtraction or elsewhere.
Square Root of 5300 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √5300?
The area of the square is 5300 square units.
Explanation
The area of the square = side^2.
The side length is given as √5300.
Area of the square = (√5300 x √5300) = 5300.
Therefore, the area of the square box is 5300 square units.
Problem 2
A square-shaped building measuring 5300 square feet is built; if each of the sides is √5300, what will be the square feet of half of the building?
2650 square feet
Explanation
We can just divide the given area by 2 as the building is square-shaped.
Dividing 5300 by 2, we get 2650.
So half of the building measures 2650 square feet.
Problem 3
Calculate √5300 x 5.
364.0055
Explanation
The first step is to find the square root of 5300, which is approximately 72.80.
The second step is to multiply 72.80 by 5.
So 72.80 x 5 ≈ 364.0055.
Problem 4
What will be the square root of (5300 + 25)?
The square root is approximately 72.839.
Explanation
To find the square root, we need to find the sum of (5300 + 25). 5300 + 25 = 5325, and then √5325 ≈ 72.839.
Therefore, the square root of (5300 + 25) is approximately ±72.839.
Problem 5
Find the perimeter of the rectangle if its length ‘l’ is √5300 units and the width ‘w’ is 38 units.
The perimeter of the rectangle is approximately 221.6 units.
Explanation
Perimeter of the rectangle = 2 × (length + width).
Perimeter = 2 × (√5300 + 38) = 2 × (72.80 + 38) = 2 × 110.8 = 221.6 units.
FAQ on Square Root of 5300
1.What is √5300 in its simplest form?
2.Mention the factors of 5300.
3.Calculate the square of 5300.
4.Is 5300 a prime number?
5.5300 is divisible by?
6.How does learning Algebra help students in Qatar make better decisions in daily life?
7.How can cultural or local activities in Qatar support learning Algebra topics such as Square Root of 5300?
8.How do technology and digital tools in Qatar support learning Algebra and Square Root of 5300?
9.Does learning Algebra support future career opportunities for students in Qatar?
Important Glossaries for the Square Root of 5300
- 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 usually the positive square root that is used, known as the principal square root.
- Prime factorization: The process of expressing a number as a product of its prime factors.
- Long division method: A step-by-step method used to find the square root of a number by dividing it into groups and finding successive approximations.
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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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