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Last updated on May 26th, 2025

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Square Root of 103

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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 the field of vehicle design, finance, etc. Here, we will discuss the square root of 103.

Square Root of 103 for Indian Students
Professor Greenline from BrightChamps

What is the Square Root of 103?

The square root is the inverse of the square of the number. 103 is not a perfect square. The square root of 103 is expressed in both radical and exponential form.

In radical form, it is expressed as √103, whereas (103)1/2 in exponential form. √103 ≈ 10.14889, 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.

Professor Greenline from BrightChamps

Finding the Square Root of 103

The prime factorization method is used for perfect square numbers. However, for non-perfect square numbers like 103, methods such as the long division method and approximation method are used. Let us now learn the following methods: -

 

  1. Long division method
  2. Approximation method
Professor Greenline from BrightChamps

Square Root of 103 by Long Division Method

The long division method is particularly used for non-perfect square numbers. This method involves finding the closest perfect square number for the given number. Let us now learn how to find the square root of 103 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 103, we treat it as a single group because it has only three digits.

 

Step 2: Now we need to find n whose square is closest to 10. We can say n is ‘3’ because 3 × 3 = 9, which is less than 10. Now the quotient is 3, and after subtracting 9 from 10, the remainder is 1.

 

Step 3: Bring down 3 next to the remainder, making it 13. Add the old divisor with the same number, 3 + 3, to get 6 as the new divisor.

 

Step 4: The new divisor is 6n. We need to find the value of n. Try n = 2, so 6 × 2 = 12, which is less than or equal to 13.

 

Step 5: Subtract 12 from 13, and the remainder is 1. The quotient becomes 10.2.

 

Step 6: Since the dividend is less than the divisor, we need to add a decimal point and bring down two zeros, making the new dividend 100.

 

Step 7: The new divisor will be 62. Try n = 1, so 62 × 1 = 62.

 

Step 8: Subtract 62 from 100, leaving a remainder of 38.

 

Step 9: Continue doing these steps until we get the desired precision.

 

We find the square root of √103 ≈ 10.14889.

Professor Greenline from BrightChamps

Square Root of 103 by Approximation Method

The approximation method is another approach 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 103 using the approximation method.

 

Step 1: Now we have to find the closest perfect squares around 103. The smallest perfect square less than 103 is 100, and the largest perfect square greater than 103 is 121. √103 falls somewhere between 10 and 11.

 

Step 2: Now we apply the formula: (Given number - smallest perfect square) / (Greater perfect square - smallest perfect square). (103 - 100) / (121 - 100) = 3 / 21 ≈ 0.143

 

Adding this value to the square root of the smaller perfect square, we get 10 + 0.143 = 10.143.

 

This approximation shows √103 ≈ 10.143.

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Common Mistakes and How to Avoid Them in the Square Root of 103

Students often make mistakes while finding the square root, such as forgetting about the negative square root and skipping steps in the long division method. Now let us look at a few of those mistakes in detail.

Mistake 1

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Forgetting about the negative square root

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It is important to remember that a number has both positive and negative square roots. However, we typically use only the positive square root, as it is the most relevant in practical applications.

For example, √103 ≈ 10.14889, but there is also -10.14889 which should not be ignored.

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Square Root of 103 Examples

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Problem 1

Can you help Mia find the area of a square box if its side length is given as √103?

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The area of the square is approximately 106.01 square units.

Explanation

The area of a square = side2.

The side length is given as √103.

Area = (√103) × (√103) ≈ 10.14889 × 10.14889 ≈ 103.01

Therefore, the area of the square box is approximately 106.01 square units.

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Max, the Girl Character from BrightChamps

Problem 2

A square-shaped garden measuring 103 square feet is built; if each of the sides is √103, what will be the square feet of half of the garden?

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51.5 square feet

Explanation

To find the area of half the garden, divide the total area by 2. 103 / 2 = 51.5

So half of the garden measures 51.5 square feet.

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Problem 3

Calculate √103 × 4.

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40.5956

Explanation

First, find the square root of 103, which is approximately 10.14889.

Then multiply by 4. 10.14889 × 4 ≈ 40.5956

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Max, the Girl Character from BrightChamps

Problem 4

What will be the square root of (103 + 16)?

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The square root is 11.

Explanation

First, find the sum of (103 + 16) = 119, then find the square root of 119, which is approximately 10.9087.

 

However, if we consider perfect squares, the closest would be 121, whose square root is 11.

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Max, the Girl Character from BrightChamps

Problem 5

Find the perimeter of a rectangle if its length 'l' is √103 units and the width 'w' is 20 units.

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The perimeter of the rectangle is approximately 60.2978 units.

Explanation

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

 

Perimeter = 2 × (√103 + 20)

 

= 2 × (10.14889 + 20) ≈ 2 × 30.14889 ≈ 60.2978 units.

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FAQ on Square Root of 103

1.What is √103 in its simplest form?

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2.Is 103 a perfect square?

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3.Calculate the square of 103.

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4.Is 103 a prime number?

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5.What is the square root of 103 rounded to the nearest whole number?

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

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7.How can cultural or local activities in India support learning Algebra topics such as Square Root of 103?

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8.How do technology and digital tools in India support learning Algebra and Square Root of 103?

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

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Professor Greenline from BrightChamps

Important Glossaries for the Square Root of 103

  • Square root: A square root is the inverse of a square. For example, 42 = 16, and the inverse of the square is the square root, which 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 number: A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself.

 

  • 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 42.

 

  • Approximation: Approximation is the process of finding a value that is close enough to the correct answer, usually within a specified tolerance.
Professor Greenline from BrightChamps

About BrightChamps in India

At BrightChamps, we see algebra as more than just symbols—it opens doors to endless opportunities! Our mission is to help children all over India develop vital math skills, focusing today on the Square Root of 103 with special attention to understanding square roots—in a way that’s engaging, lively, and easy to follow. Whether your child is calculating the speed of a passing train, keeping scores during a cricket match, or managing pocket money for the latest gadgets, mastering algebra gives them the confidence needed for everyday situations. Our interactive lessons keep learning simple and fun. As kids in India have varied learning styles, we personalize our approach to match each child. From the busy markets of Mumbai to Delhi’s vibrant streets, BrightChamps brings math to life, making it relatable and exciting throughout India. Let’s make square roots a joyful 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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Fun Fact

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

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