128 LearnersLast updated on May 26th, 2025
Square Root of 5476
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 5476.
What is the Square Root of 5476?
The square root is the inverse of the square of the number. 5476 is a perfect square. The square root of 5476 is expressed in both radical and exponential form. In the radical form, it is expressed as √5476, whereas (5476)^(1/2) in the exponential form. √5476 = 74, which is a rational number because it can be expressed in the form of p/q, where p and q are integers and q ≠ 0.
Finding the Square Root of 5476
The prime factorization method can be used for perfect square numbers. For non-perfect squares, the long-division method and approximation method are used. Let us now learn the methods:
- Prime factorization method
- Long division method
- Approximation method
Square Root of 5476 by Prime Factorization Method
The product of prime factors is the prime factorization of a number. Now let us look at how 5476 is broken down into its prime factors:
Step 1: Finding the prime factors of 5476 Breaking it down, we get 2 x 2 x 41 x 41: 2^2 x 41^2
Step 2: Now we found out the prime factors of 5476. The next step is to make pairs of those prime factors. Since 5476 is a perfect square, the digits of the number can be grouped in pairs.
Therefore, √5476 = 2 x 41 = 82.
Square Root of 5476 by Long Division Method
The long division method is particularly used for 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 5476, we group it as 54 and 76.
Step 2: Now we need to find n whose square is less than or equal to 54. We can say n is 7 because 7 x 7 = 49, which is less than 54. The quotient is 7, and the remainder is 54 - 49 = 5.
Step 3: Bring down 76, making the new dividend 576. Add the old divisor with the same number 7 + 7 to get 14 as our new divisor.
Step 4: We need to find the value of n such that 14n x n ≤ 576. Let n be 4, then 144 x 4 = 576.
Step 5: Subtracting 576 - 576 gives a remainder of 0.
Step 6: The quotient is 74.
So the square root of √5476 is 74.
Square Root of 5476 by Approximation Method
The approximation method is an easy method for finding the square roots. Here’s how to approximate the square root of 5476.
Step 1: Find the closest perfect square of √5476. The square root of 5476 is exactly 74, so the approximation method is not needed in this case since 5476 is a perfect square.
Common Mistakes and How to Avoid Them in the Square Root of 5476
Students make mistakes while finding the square root, such as forgetting about the negative square root or skipping steps in the long division method. Let us look at a few common mistakes and how to avoid them.
Mistake 1
Forgetting about the negative square root
It is important to remember that a number has both positive and negative square roots. However, we usually consider only the positive square root.
For example, √5476 = 74, but there is also -74, which should not be forgotten.
Mistake 2
Not adding the square root symbol in proper places
Using the square root symbol properly is crucial. Simplify the numbers inside the square root first.
For example, √(5476) = 74 is correct, while √(5476) = 2 x 41 without simplification is incorrect.
Mistake 3
Not finding the correct value of a non-perfect square
The first step is to simplify the numbers inside the square root. This ensures that students find the correct approximate value.
For example, √5476 = 74 is correct, while √5476 = 75 is incorrect.
Mistake 4
Confusing the square root symbol with the cube root
Students need to distinguish between cube root and square root to avoid errors.
For example, √5476 and ∛5476 are different.
Mistake 5
Making mistakes in long division
Finding a square root using the long division method involves several steps, and students may skip a step accidentally, resulting in an incorrect answer. Care must be taken with each step.
Square Root of 5476 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √5476?
The area of the square is 5476 square units.
Explanation
The area of the square = side².
The side length is given as √5476.
Area of the square = side² = (√5476) x (√5476) = 74 x 74 = 5476.
Therefore, the area of the square box is 5476 square units.
Problem 2
A square-shaped building measuring 5476 square feet is built; if each of the sides is √5476, what will be the square feet of half of the building?
2738 square feet
Explanation
Since the building is square-shaped, we can divide the given area by 2.
Dividing 5476 by 2 = 2738.
So half of the building measures 2738 square feet.
Problem 3
Calculate √5476 x 5.
370
Explanation
The first step is to find the square root of 5476, which is 74.
The second step is to multiply 74 by 5.
So 74 x 5 = 370.
Problem 4
What will be the square root of (5476 + 24)?
The square root is 75.
Explanation
To find the square root, we need to find the sum of (5476 + 24). 5476 + 24 = 5500, and √5500 is approximately 74.16.
Therefore, the square root of (5476 + 24) is approximately ±74.16.
Problem 5
Find the perimeter of the rectangle if its length ‘l’ is √5476 units and the width ‘w’ is 38 units.
The perimeter of the rectangle is 224 units.
Explanation
Perimeter of the rectangle = 2 × (length + width)
Perimeter = 2 × (√5476 + 38) = 2 × (74 + 38) = 2 × 112 = 224 units.
FAQ on Square Root of 5476
1.What is √5476 in its simplest form?
2.Mention the factors of 5476.
3.Calculate the square of 74.
4.Is 5476 a prime number?
5.5476 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 5476?
8.How do technology and digital tools in India support learning Algebra and Square Root of 5476?
9.Does learning Algebra support future career opportunities for students in India?
Important Glossaries for the Square Root of 5476
- Square root: A square root is the inverse of a square. Example: 8^2 = 64, and the inverse of the square is the square root, that is √64 = 8.
- Perfect square: A perfect square is a number that is the square of an integer. For example, 5476 is a perfect square because √5476 = 74.
- Rational number: A rational number can be expressed as the quotient or fraction p/q of two integers, where q is not zero.
- Integer: An integer is a whole number that can be positive, negative, or zero. For example, -3, 0, 2, 74 are integers.
- Factor: A factor is a number that divides another number without a remainder. For example, 2 is a factor of 4.
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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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