101 LearnersLast updated on May 26th, 2025
Square Root of 1/100
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 1/100.
What is the Square Root of 1/100?
The square root is the inverse of the square of the number. 1/100 is a perfect square. The square root of 1/100 is expressed in both radical and exponential form. In the radical form, it is expressed as √(1/100), whereas (1/100)^(1/2) in exponential form. √(1/100) = 1/10 = 0.1, which is a rational number because it can be expressed in the form of p/q, where p and q are integers and q ≠ 0.
Finding the Square Root of 1/100
The prime factorization method can be used for finding the square roots of perfect squares. However, for fractions like 1/100, we use the property of square roots of fractions: √(a/b) = √a/√b. Let us now learn the following methods: Fraction property method Approximation method
Square Root of 1/100 by Fraction Property Method
The fraction property method uses the property of square roots of fractions. Now let us look at how 1/100 is simplified using this method.
Step 1: Express 1/100 as a fraction.
Step 2: Apply the square root property: √(1/100) = √1/√100.
Step 3: Calculate the square roots separately: √1 = 1 and √100 = 10.
Step 4: Divide the results: 1/10 = 0.1. Therefore, √(1/100) = 0.1.
Square Root of 1/100 by Approximation Method
The approximation method can be used to find the square roots of non-perfect squares or to verify our calculations. However, since 1/100 is a perfect square, the exact method is more straightforward. Yet, for understanding, let's see the approximation approach.
Step 1: Recognize that 1/100 is a small fraction close to zero.
Step 2: Approximate √(1/100) by recognizing it is between √0 and √0.25.
Step 3: Use the known values: √0.25 = 0.5 and √0 = 0 to approximate 0.1. T
herefore, √(1/100) approximates to 0.1, confirming our exact calculation.
Common Mistakes and How to Avoid Them in the Square Root of 1/100
Students make mistakes while finding the square root, such as forgetting about the negative square root, confusing fractions, etc. Now let us look at a few of those mistakes that students tend to make in detail.
Mistake 1
Forgetting about the negative square root
It is important to make students aware that a number does have both positive and negative square roots. However, we will be taking only the positive square root, as it is the required one.
For example: √(1/100) = 0.1, there is also -0.1 which should not be forgotten.
Square Root of 1/100 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √(1/16)?
The area of the square is 1/16 square units.
Explanation
The area of the square = side^2.
The side length is given as √(1/16).
Area of the square = side^2 = √(1/16) × √(1/16) = 1/4 × 1/4 = 1/16.
Therefore, the area of the square box is 1/16 square units.
Problem 2
A square-shaped building measuring 1/100 square feet is built; if each of the sides is √(1/100), what will be the square feet of half of the building?
1/200 square feet
Explanation
We can just divide the given area by 2 as the building is square-shaped.
Dividing 1/100 by 2 = 1/200.
So half of the building measures 1/200 square feet.
Problem 3
Calculate √(1/100) × 5.
0.5
Explanation
The first step is to find the square root of 1/100 which is 0.1, the second step is to multiply 0.1 with 5. So 0.1 × 5 = 0.5.
Problem 4
What will be the square root of (1/16 + 1/16)?
The square root is 1/4
Explanation
To find the square root, we need to find the sum of (1/16 + 1/16). 1/16 + 1/16 = 1/8, and then √(1/8) = 1/√8 = 1/√(4×2) = 1/(2√2) = 1/4 when simplified for this context. Therefore, the square root of (1/16 + 1/16) is ±1/4.
Problem 5
Find the perimeter of the rectangle if its length ‘l’ is √(1/16) units and the width ‘w’ is 3 units.
We find the perimeter of the rectangle as 6.5 units.
Explanation
Perimeter of the rectangle = 2 × (length + width). Perimeter = 2 × (√(1/16) + 3) = 2 × (1/4 + 3) = 2 × (0.25 + 3) = 2 × 3.25 = 6.5 units.
FAQ on Square Root of 1/100
1.What is √(1/100) in its simplest form?
2.Mention the factors of 1/100.
3.Calculate the square of 1/100.
4.Is 1/100 a prime number?
5.1/100 is divisible by?
Important Glossaries for the Square Root of 1/100
- Square root: A square root is the inverse of a square. Example: 4^2 = 16 and the inverse of the square is the square root, that is √16 = 4.
- Rational number: A rational number is a number that can be written in the form of p/q, where q is not equal to zero and p and q are integers.
- Perfect square: A perfect square is a number that is the square of an integer. For example, 100 is a perfect square as it is 10^2.
- Fraction: A fraction is a part of a whole expressed as a numerator over a denominator. Example: 1/2, 3/4, etc.
- Decimal: If a number has a whole number and a fraction in a single number then it is called a decimal. For example, 0.1, 0.75, and 2.5 are decimals.
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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.
