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Last updated on May 26th, 2025

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Square Root of 496

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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 architecture, finance, etc. Here, we will discuss the square root of 496.

Square Root of 496 for Filipino Students
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What is the Square Root of 496?

The square root is the inverse of the square of a number. 496 is not a perfect square. The square root of 496 is expressed in both radical and exponential form. In radical form, it is expressed as √496, whereas in exponential form it is expressed as (496)^(1/2). √496 ≈ 22.27106, 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.

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Finding the Square Root of 496

For perfect square numbers, the prime factorization method can be used. However, for non-perfect square numbers, methods such as the long division method and approximation method are used. Let us now learn the following methods:

 

  • Prime factorization method
  • Long division method
  • Approximation method
Professor Greenline from BrightChamps

Square Root of 496 by Prime Factorization Method

The prime factorization of a number is the product of its prime factors. Now let us look at how 496 is broken down into its prime factors.

 

Step 1: Finding the prime factors of 496 Breaking it down, we get 2 x 2 x 2 x 2 x 31: 2^4 x 31

 

Step 2: Now we have found the prime factors of 496. The second step is to make pairs of these prime factors. Since 496 is not a perfect square, the digits of the number can’t be grouped in pairs. Therefore, calculating √496 using prime factorization alone is not straightforward.

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Square Root of 496 by Long Division Method

The long division method is particularly useful 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 496, we group it as 96 and 4.

 

Step 2: Now, we need to find n whose square is ≤ 4. We can say n is ‘2’ because 2 x 2 is less than or equal to 4. The quotient is 2, and after subtracting, the remainder is 0.

 

Step 3: Now bring down 96, making it the new dividend. Add the old divisor with the same number 2 + 2 to get 4, which will be our new divisor.

 

Step 4: The new divisor will be the sum of the dividend and quotient. We now have 4n as the new divisor and need to find the value of n.

 

Step 5: Find 4n x n ≤ 96; let n be 2, now 4 x 2 x 2 = 16.

 

Step 6: Subtract 96 from 16 to get 80, and the quotient is 22.

 

Step 7: Since the dividend is less than the divisor, add a decimal point. Adding the decimal point allows us to bring down two zeros to the dividend. Now the new dividend is 8000.

 

Step 8: The new divisor is 44 because 442 x 2 = 884.

 

Step 9: Subtracting 884 from 8000 gives 7116 as the result.

 

Step 10: Now the quotient is approximately 22.27.

 

Step 11: Continue these steps until you get two numbers after the decimal point. If there is no decimal value, continue until the remainder is zero.

 

So the square root of √496 is approximately 22.27.

Professor Greenline from BrightChamps

Square Root of 496 by Approximation Method

The approximation method is another method for finding square roots; it is an easy way to find the square root of a given number. Now let us learn how to find the square root of 496 using the approximation method.

 

Step 1: Find the closest perfect squares to √496. The smallest perfect square less than 496 is 484, and the largest perfect square greater than 496 is 529. √496 falls somewhere between 22 and 23.

 

Step 2: Apply the formula: (Given number - smallest perfect square) / (Greater perfect square - smallest perfect square). Using the formula, (496 - 484) / (529 - 484) = 12 / 45 ≈ 0.27. Adding this to the integer part gives us 22 + 0.27 = 22.27.

 

So the square root of 496 is approximately 22.27.

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Common Mistakes and How to Avoid Them in the Square Root of 496

Students often make mistakes while finding the square root, such as forgetting about the negative square root or skipping steps in the long division method, etc. Let us look at a few of these mistakes in detail.

Mistake 1

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Forgetting about the negative square root

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It is important to remind students that a number has both positive and negative square roots. However, we typically consider only the positive square root as it is often the required one.

For example, √50 ≈ 7.07, but there is also -7.07, which should not be forgotten.

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Square Root of 496 Examples

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Max, the Girl Character from BrightChamps

Problem 1

Can you help Max find the area of a square box if its side length is given as √496?

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The area of the square is 496 square units.

Explanation

The area of a square = side^2.

The side length is given as √496.

Area of the square = side^2 = √496 x √496 = 496.

Therefore, the area of the square box is 496 square units.

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Max, the Girl Character from BrightChamps

Problem 2

A square-shaped building measuring 496 square feet is built; if each of the sides is √496, what will be the square feet of half of the building?

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248 square feet

Explanation

We can divide the given area by 2 as the building is square-shaped.

Dividing 496 by 2 = 248.

So half of the building measures 248 square feet.

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Max, the Girl Character from BrightChamps

Problem 3

Calculate √496 x 5.

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111.35

Explanation

The first step is to find the square root of 496, which is approximately 22.27.

The second step is to multiply 22.27 by 5.

So 22.27 x 5 = 111.35.

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Max, the Girl Character from BrightChamps

Problem 4

What will be the square root of (496 + 16)?

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The square root is 23.

Explanation

To find the square root, we need to find the sum of (496 + 16). 496 + 16 = 512, and then √512 ≈ 22.63.

Therefore, the square root of (496 + 16) is approximately 22.63.

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Max, the Girl Character from BrightChamps

Problem 5

Find the perimeter of the rectangle if its length ‘l’ is √496 units and the width ‘w’ is 38 units.

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We find the perimeter of the rectangle as 120.54 units.

Explanation

Perimeter of the rectangle = 2 × (length + width)

Perimeter = 2 × (√496 + 38) ≈ 2 × (22.27 + 38) = 2 × 60.27 = 120.54 units.

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FAQ on Square Root of 496

1.What is √496 in its simplest form?

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2.Mention the factors of 496.

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3.Calculate the square of 496.

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4.Is 496 a prime number?

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5.496 is divisible by?

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6.How does learning Algebra help students in Philippines make better decisions in daily life?

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7.How can cultural or local activities in Philippines support learning Algebra topics such as Square Root of 496?

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8.How do technology and digital tools in Philippines support learning Algebra and Square Root of 496?

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9.Does learning Algebra support future career opportunities for students in Philippines?

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Professor Greenline from BrightChamps

Important Glossaries for the Square Root of 496

  • 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.
     
  • Prime factorization: The process of expressing a number as a product of its prime factors.
     
  • Approximation method: A method used to find an approximate value of a square root or other mathematical expression.
     
  • Long division method: A step-by-step method used to find the square root of a non-perfect square number.
Professor Greenline from BrightChamps

About BrightChamps in Philippines

At BrightChamps, we believe algebra is more than symbols—it’s a gateway to countless opportunities! Our mission is to support children across the Philippines in mastering key math skills, focusing today on the Square Root of 496 with an emphasis on understanding square roots—in a lively, fun, and easy-to-follow way. Whether your child is calculating the speed of a roller coaster at Enchanted Kingdom, tracking basketball scores, or managing their allowance to buy the latest gadgets, mastering algebra builds their confidence for daily challenges. Our hands-on lessons make learning simple and enjoyable. Since kids in the Philippines learn in different styles, we tailor our approach to each learner. From Manila’s busy streets to the beautiful islands of Palawan, BrightChamps brings math to life, making it exciting and relevant throughout the Philippines. Let’s make square roots a fun part of every child’s math journey!
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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.

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Max, the Girl Character from BrightChamps

Fun Fact

: He loves to play the quiz with kids through algebra to make kids love it.

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