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Last updated on May 26th, 2025

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Square Root of 1/10

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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 various fields such as engineering, physics, and finance. Here, we will discuss the square root of 1/10.

Square Root of 1/10 for UAE Students
Professor Greenline from BrightChamps

What is the Square Root of 1/10?

The square root is the inverse of the square of a number. 1/10 is not a perfect square. The square root of 1/10 is expressed in both radical and exponential form. In the radical form, it is expressed as √(1/10), whereas (1/10)^(1/2) in the exponential form. √(1/10) = 0.316227766, 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 1/10

The prime factorization method is used for perfect square numbers. 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:

 

  • Long division method
  • Approximation method
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Square Root of 1/10 by Long Division Method

The long division method is particularly used for non-perfect square numbers. In this method, we approximate the square root to a desired precision. Let us now learn how to find the square root using the long division method, step by step.

 

Step 1: Convert 1/10 to a decimal, which is 0.1.

 

Step 2: Group the numbers from right to left in pairs. Here, 0.1 is grouped as 0.10.

 

Step 3: Find the largest number whose square is less than or equal to 10. In this case, 3 × 3 = 9 is the closest.

 

Step 4: Subtract 9 from 10, giving a remainder of 1. Bring down two zeros to get 100.

 

Step 5: Double the divisor (3), giving 6.

 

Step 6: Find the largest digit (d) such that (60 + d) × d ≤ 100. Here, d = 1 makes (60 + 1) × 1 = 61 ≤ 100.

 

Step 7: Subtract 61 from 100 to get a remainder of 39. Bring down another pair of zeros to get 3900.

 

Step 8: Repeat the process to achieve the desired precision.

 

The square root of 0.1 using the long division method is approximately 0.316.

Professor Greenline from BrightChamps

Square Root of 1/10 by Approximation Method

The approximation method is another method for finding square roots. It is a simpler method to find the square root of a given number. Let us learn how to find the square root of 1/10 using the approximation method.

 

Step 1: Consider the closest perfect squares around 0.1. The closest perfect squares are 0 and 0.25.

 

Step 2: The square root of 0 is 0, and the square root of 0.25 is 0.5.

 

Step 3: 0.1 lies between these two values, so the square root of 0.1 lies between 0 and 0.5.

 

Step 4: By approximation, the square root of 0.1 is closer to the square root of 0.25.

 

So we approximate it as 0.316.

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Common Mistakes and How to Avoid Them in the Square Root of 1/10

Students can make mistakes while finding the square root, such as forgetting about the negative square root or confusing methods. Let's explore some common 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 the principal (positive) square root.

For example, √0.1 = 0.316227766, but there is also -0.316227766.

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Square Root of 1/10 Examples

Ray, the Character from BrightChamps Explaining Math Concepts
Max, the Girl Character from BrightChamps

Problem 1

Can you help Max find the length of the side of a square whose area is 1/10 square units?

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The side length of the square is approximately 0.31623 units.

Explanation

The side length of a square is the square root of its area.

Therefore, the side length is √(1/10) ≈ 0.31623 units.

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Max, the Girl Character from BrightChamps

Problem 2

A square-shaped floor has an area of 1/10 square meters. What is the perimeter of the floor?

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The perimeter of the floor is approximately 1.26492 meters.

Explanation

The side length of the floor is √(1/10) ≈ 0.31623 meters.

The perimeter of a square is 4 times its side length.

Thus, the perimeter is 4 × 0.31623 ≈ 1.26492 meters.

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Max, the Girl Character from BrightChamps

Problem 3

Calculate √(1/10) × 5.

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The result is approximately 1.58114.

Explanation

First, find the square root of 1/10, which is approximately 0.31623.

Then multiply by 5: 0.31623 × 5 ≈ 1.58114.

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Max, the Girl Character from BrightChamps

Problem 4

What will be the square root of (1/10) + 0.15?

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The square root is approximately 0.5.

Explanation

First, calculate the sum: (1/10) + 0.15 = 0.25.

The square root of 0.25 is 0.5.

Therefore, the square root of (1/10) + 0.15 is ±0.5.

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Max, the Girl Character from BrightChamps

Problem 5

Find the diagonal of a square with an area of 1/10 square units.

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The diagonal is approximately 0.44721 units.

Explanation

The side length of the square is √(1/10) ≈ 0.31623 units.

The diagonal of a square is √2 times the side length.

Therefore, the diagonal is √2 × 0.31623 ≈ 0.44721 units.

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FAQ on Square Root of 1/10

1.What is √(1/10) in its simplest form?

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2.Is 1/10 a perfect square?

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3.What is the square of 1/10?

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4.Is 1/10 a rational number?

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5.How is the square root of 1/10 useful?

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6.How does learning Algebra help students in United Arab Emirates make better decisions in daily life?

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7.How can cultural or local activities in United Arab Emirates support learning Algebra topics such as Square Root of 1/10?

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8.How do technology and digital tools in United Arab Emirates support learning Algebra and Square Root of 1/10?

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9.Does learning Algebra support future career opportunities for students in United Arab Emirates?

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Professor Greenline from BrightChamps

Important Glossaries for the Square Root of 1/10

  • Square root: The square root is the inverse of a square. For example, 0.31623 is the square root of 0.1 as 0.31623^2 = 0.1.
     
  • Irrational number: An irrational number cannot be written in the form p/q, where p and q are integers, and q is not zero. For example, √(1/10) is irrational.
     
  • Principal square root: The principal square root is the positive square root of a number, often used in practical applications.
     
  • Decimal: A decimal is a number with a whole number and fractional part separated by a decimal point, such as 0.31623.
     
  • Long division method: A method used to find square roots of non-perfect squares by approximating them to a desired precision using division steps.
Professor Greenline from BrightChamps

About BrightChamps in United Arab Emirates

At BrightChamps, we know algebra is more than symbols—it opens doors to endless possibilities! We’re dedicated to helping kids throughout the UAE develop crucial math skills, focusing today on the Square Root of 1/10 with a special focus on square roots—in an enjoyable, engaging, and easy-to-understand way. Whether your child is figuring out the speed of a roller coaster at Dubai Parks and Resorts, keeping track of local football scores, or budgeting their allowance for the latest gadgets, mastering algebra gives them confidence for everyday situations. Our interactive lessons make learning both fun and simple. Because kids in the UAE learn in varied ways, we customize our teaching to fit each child’s needs. From Dubai’s soaring skyscrapers to Abu Dhabi’s cultural heritage, BrightChamps brings math alive, making it relevant and exciting throughout the UAE. 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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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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