118 LearnersLast updated on May 26th, 2025
Square Root of 5248
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 and finance. Here, we will discuss the square root of 5248.
What is the Square Root of 5248?
The square root is the inverse of the square of the number. 5248 is not a perfect square. The square root of 5248 is expressed in both radical and exponential form. In the radical form, it is expressed as √5248, whereas (5248)^(1/2) in the exponential form. √5248 ≈ 72.44493, 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 5248
The prime factorization method is used for perfect square numbers. However, for non-perfect square numbers like 5248, 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 5248 by Prime Factorization Method
The product of prime factors is the prime factorization of a number. Now let us look at how 5248 is broken down into its prime factors.
Step 1: Finding the prime factors of 5248
Breaking it down, we get 2 x 2 x 2 x 2 x 2 x 2 x 41: 2^6 x 41
Step 2: Now we found out the prime factors of 5248. The second step is to make pairs of those prime factors. Since 5248 is not a perfect square, the digits of the number can’t be grouped into pairs completely. Therefore, calculating 5248 using prime factorization directly is not possible.
Square Root of 5248 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 5248, we need to group it as 48 and 52.
Step 2: Now we need to find n whose square is closest to 52. We can say n as ‘7’ because 7 x 7 = 49, which is less than 52. Now the quotient is 7, and after subtracting 49 from 52, the remainder is 3.
Step 3: Now let us bring down 48, which is the new dividend. Add the old divisor with the same number 7 + 7, we get 14, which will be our new divisor.
Step 4: The new divisor will be 14n. We need to find the value of n such that 14n x n ≤ 348.
Step 5: By trial, finding 14 x 2 x 2 = 56, we see 14 x 2 = 28 is too small. Trying 14 x 5 = 70, we find 70 x 5 = 350, slightly over. So, 70 x 4 = 280 fits.
Step 6: Subtract 280 from 348, the difference is 68, and the quotient becomes 74.
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 6800.
Step 8: Now we need to find the new divisor that is 149 because 149 x 4 = 596, and 149 x 5 = 745, so 149 x 4 fits closest.
Step 9: Subtracting 596 from 6800, we get the result 204.
Step 10: Continue doing these steps until we get two numbers after the decimal point.
So the square root of √5248 is approximately 72.44.
Square Root of 5248 by Approximation Method
The approximation method is another method for finding square roots, and 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 5248 using the approximation method.
Step 1: Now we have to find the closest perfect square of √5248. The smallest perfect square less than 5248 is 4900 and the largest perfect square greater than 5248 is 5625. √5248 falls somewhere between 70 and 75.
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 (5248 - 4900) ÷ (5625 - 4900) = 348 ÷ 725 ≈ 0.48. 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 + 0.48 = 70.48, so the square root of 5248 is approximately 72.44.
Common Mistakes and How to Avoid Them in the Square Root of 5248
Students do make mistakes while finding the square root, such as forgetting about the negative square root or skipping steps in long division methods. 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 often only consider the positive square root due to its practical applications.
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. To resolve this, teach children that simplifying the numbers inside the square root is important before proceeding.
For example: √(12+24) = √36 is correct, whereas √12 + √24 is incorrect.
Mistake 3
Not finding the correct value of a non-perfect square
The first step is to simplify numbers inside the square root. This is important to avoid mistakes while identifying the approximate value.
For example: √50 ≈ 7.071067, not 7.
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.
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, students might skip a step accidentally, resulting in a wrong answer at the end. This may either happen in subtracting or elsewhere.
Square root of 5248 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √5248?
The area of the square is approximately 275,162.304 square units.
Explanation
The area of the square = side^2.
The side length is given as √5248.
Area of the square = side^2 = √5248 x √5248 = 72.44493 x 72.44493 ≈ 275,162.304
Problem 2
A square-shaped building measuring 5248 square feet is built; if each of the sides is √5248, what will be the square feet of half of the building?
2624 square feet
Explanation
We can just divide the given area by 2 as the building is square-shaped.
Dividing 5248 by 2, we get 2624.
Problem 3
Calculate √5248 x 5.
Approximately 362.22465
Explanation
The first step is to find the square root of 5248, which is approximately 72.44493.
The second step is to multiply 72.44493 by 5.
So 72.44493 x 5 ≈ 362.22465
Problem 4
What will be the square root of (5248 + 152)?
The square root is approximately 74.40
Explanation
To find the square root, we need to find the sum of (5248 + 152). 5248 + 152 = 5400, and then √5400 ≈ 74.40.
Problem 5
Find the perimeter of the rectangle if its length ‘l’ is √5248 units and the width ‘w’ is 38 units.
The perimeter of the rectangle is approximately 220.89 units.
Explanation
Perimeter of the rectangle = 2 × (length + width).
Perimeter = 2 × (√5248 + 38) = 2 × (72.44493 + 38) ≈ 2 × 110.44493 ≈ 220.89 units.
FAQ on Square Root of 5248
1.What is √5248 in its simplest form?
2.Mention the factors of 5248.
3.Calculate the square of 5248.
4.Is 5248 a prime number?
5.5248 is divisible by?
6.How does learning Algebra help students in Singapore make better decisions in daily life?
7.How can cultural or local activities in Singapore support learning Algebra topics such as Square Root of 5248?
8.How do technology and digital tools in Singapore support learning Algebra and Square Root of 5248?
9.Does learning Algebra support future career opportunities for students in Singapore?
Important Glossaries for the Square Root of 5248
- Square root: A square root is the inverse of a square. For 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.
- Approximation: Approximating involves estimating a number to a suitable degree of accuracy. For example, √2 ≈ 1.414.
- Perfect square: A perfect square is a number that is the square of an integer. For example, 16 is a perfect square because it is 4^2.
- Exponent: An exponent refers to the number of times a number is multiplied by itself. For example, in 2^3, 3 is the exponent, indicating that 2 is multiplied by itself three times.
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About BrightChamps in Singapore
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.
