130 LearnersLast updated on May 26th, 2025
Square Root of 1/10
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.
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.
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
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.
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.
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
Forgetting about the negative square root
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.
Mistake 2
Not adding the square root symbol in proper places
Improper use of the square root symbol is another common mistake. It's crucial to simplify the expression inside the square root before proceeding.
For example, √(1/10) means the square root of the entire fraction, not √1/√10.
Mistake 3
Not finding the correct value of a non-perfect square
When approximating the square root of a non-perfect square, it's important to simplify the number first.
For example, √0.1 ≈ 0.316227766 instead of approximating incorrectly.
Mistake 4
Confusing the square root symbol with the cube root
Students need to understand the difference between cube roots and square roots.
For example, √0.1 and ∛0.1 are different and have different values.
Mistake 5
Making mistakes in long division
Finding a square root using the long division method involves multiple steps. Students might skip a step accidentally, resulting in an incorrect answer. It's important to follow each step carefully.
Square Root of 1/10 Examples
Problem 1
Can you help Max find the length of the side of a square whose area is 1/10 square units?
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.
Problem 2
A square-shaped floor has an area of 1/10 square meters. What is the perimeter of the floor?
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.
Problem 3
Calculate √(1/10) × 5.
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.
Problem 4
What will be the square root of (1/10) + 0.15?
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.
Problem 5
Find the diagonal of a square with an area of 1/10 square units.
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.
FAQ on Square Root of 1/10
1.What is √(1/10) in its simplest form?
2.Is 1/10 a perfect square?
3.What is the square of 1/10?
4.Is 1/10 a rational number?
5.How is the square root of 1/10 useful?
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.
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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
: He loves to play the quiz with kids through algebra to make kids love it.
