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Last updated on May 26th, 2025

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Square Root of 10496

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If a number is multiplied by itself, the result is a square. The inverse operation is finding the square root. The square root is applied in various fields like engineering, physics, and finance. Here, we will discuss the square root of 10496.

Square Root of 10496 for Bahraini Students
Professor Greenline from BrightChamps

What is the Square Root of 10496?

The square root is the inverse operation of squaring a number. 10496 is not a perfect square. The square root of 10496 is expressed in both radical and exponential forms. In radical form, it is expressed as √10496, whereas in exponential form, it is expressed as (10496)^(1/2). √10496 equals approximately 102.455, which is an irrational number because it cannot be expressed as a fraction p/q, where p and q are integers and q ≠ 0.

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Finding the Square Root of 10496

For perfect squares, the prime factorization method is used. For non-perfect squares like 10496, the long division method and approximation method are commonly used. Let us explore the following methods:

 

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

Square Root of 10496 by Prime Factorization Method

The prime factorization of a number is the product of its prime factors. Let's break down 10496 into its prime factors:

 

Step 1: Finding the prime factors of 10496.

 

Breaking it down, we get 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 41: 2^8 x 41.

 

Step 2: We found the prime factors of 10496. The second step is to make pairs of those prime factors. Since 10496 is not a perfect square, the digits of the number can’t be grouped into equal pairs completely. Thus, calculating 10496 using prime factorization yields no exact integer square root.

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Square Root of 10496 by Long Division Method

The long division method is used particularly for non-perfect squares. Let's find the square root using this method, step by step:

 

Step 1: To begin, group the numbers from right to left. For 10496, group it as 96 and 104.

 

Step 2: Find n whose square is the largest perfect square ≤ 104. Here, n = 10, since 10 x 10 = 100. Subtract 100 from 104 to get a remainder of 4. Bring down 96 to get 496.

 

Step 3: Double the quotient (10) to get 20, which will be part of the new divisor.

 

Step 4: Find a digit x such that 20x x x ≤ 496. Here, x = 2, since 202 x 2 = 404.

 

Step 5: Subtract 404 from 496 to get a remainder of 92.

 

Step 6: Since the dividend is less than the divisor, add a decimal point and bring down two zeros. Now the new dividend is 9200.

 

Step 7: Find x such that 204x x x ≤ 9200. Here, x = 4, since 2044 x 4 = 8176.

 

Step 8: Subtract 8176 from 9200, leaving a remainder of 1024.

 

Step 9: The quotient is 102.4. Continue these steps until the desired precision is achieved.

 

The square root of √10496 is approximately 102.455.

Professor Greenline from BrightChamps

Square Root of 10496 by Approximation Method

The approximation method is another way to find square roots. Here's how to find the square root of 10496 using this method:

 

Step 1: Determine the closest perfect squares around 10496. The closest perfect squares are 10404 (102^2) and 10609 (103^2). So, √10496 is between 102 and 103.

 

Step 2: Use interpolation: (Given number - smaller perfect square) / (larger perfect square - smaller perfect square). (10496 - 10404) / (10609 - 10404) = 92 / 205 ≈ 0.448 Add this value to the smaller root: 102 + 0.448 = 102.448 Thus, the approximated square root of 10496 is 102.448.

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Common Mistakes and How to Avoid Them in the Square Root of 10496

Students may make mistakes when finding square roots, such as forgetting about the negative square root or skipping steps in the long division method. Let's explore these common mistakes in detail.

Mistake 1

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Forgetting about the negative square root

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Students should be aware that numbers have both positive and negative square roots. However, we often use the positive square root in practical applications.

For example, √81 = 9 also includes -9, which should not be ignored in theoretical contexts.

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Square Root of 10496 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 √10496?

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The area of the square is 10496 square units.

Explanation

The area of a square = side^2.

The side length is given as √10496.

Area of the square = side^2 = √10496 x √10496 = 10496.

Therefore, the area of the square box is 10496 square units.

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Max, the Girl Character from BrightChamps

Problem 2

A square-shaped building measuring 10496 square feet is built; if each of the sides is √10496, what will be the square feet of half of the building?

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5248 square feet

Explanation

For a square-shaped building, simply divide the given area by 2. 10496 / 2 = 5248

So half of the building measures 5248 square feet.

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Max, the Girl Character from BrightChamps

Problem 3

Calculate √10496 x 5.

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Approximately 512.275

Explanation

First, find the square root of 10496, which is approximately 102.455.

Multiply this by 5. 102.455 x 5 = 512.275

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Max, the Girl Character from BrightChamps

Problem 4

What will be the square root of (10400 + 96)?

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The square root is approximately 102.455.

Explanation

To find the square root, calculate the sum (10400 + 96) = 10496, and then √10496 ≈ 102.455.

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Max, the Girl Character from BrightChamps

Problem 5

Find the perimeter of a rectangle if its length ‘l’ is √10496 units and the width ‘w’ is 38 units.

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The perimeter of the rectangle is approximately 280.91 units.

Explanation

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

Perimeter = 2 × (√10496 + 38) = 2 × (102.455 + 38) = 2 × 140.455 = 280.91 units.

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FAQ on Square Root of 10496

1.What is √10496 in its simplest form?

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2.Mention the factors of 10496.

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3.Calculate the square of 10496.

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4.Is 10496 a prime number?

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5.10496 is divisible by?

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

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7.How can cultural or local activities in Bahrain support learning Algebra topics such as Square Root of 10496?

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8.How do technology and digital tools in Bahrain support learning Algebra and Square Root of 10496?

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

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Professor Greenline from BrightChamps

Important Glossaries for the Square Root of 10496

  • Square root: A square root is the inverse operation of squaring a number. Example: 5^2 = 25, and thus √25 = 5.
     
  • Irrational number: An irrational number cannot be expressed as a fraction p/q, where q is not zero and p and q are integers. Example: √2 is irrational.
     
  • Perfect square: A number that is the square of an integer. Example: 36 is a perfect square because it is 6^2.
     
  • Prime factorization: The expression of a number as the product of its prime factors. Example: 18 = 2 x 3^2.
     
  • Long division method: A technique to find the square root of a number by performing division in a step-by-step manner.
Professor Greenline from BrightChamps

About BrightChamps in Bahrain

At BrightChamps, we understand algebra as more than symbols—it’s a gateway to countless opportunities! We are dedicated to helping children across Bahrain master essential math skills, focusing today on the Square Root of 10496 with special attention to square roots—in a fun, lively, and easy-to-follow manner. Whether your child is figuring out the speed of a roller coaster at Bahrain’s Wahooo! Waterpark, following local football scores, or managing their allowance to buy the latest gadgets, mastering algebra builds confidence for daily challenges. Our hands-on lessons make learning simple and enjoyable. Because kids in Bahrain learn differently, we customize our teaching to fit each learner’s style. From Manama’s lively city life to peaceful beaches, BrightChamps brings math to life, making it exciting throughout Bahrain. 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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