131 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.
Mistake 2
Confusing with decimal representation
Not converting the fraction to a decimal is another mistake that children make. To resolve this, we need to teach children to simplify the fraction first and then convert to a decimal.
For example: 1/100 = 0.01, and √(0.01) = 0.1.
Mistake 3
Misapplying fraction properties
The first step that needs to be taught to children is the correct application of square root properties for fractions. This is important so that students do not make mistakes while simplifying.
For example: √(1/4) = 1/2 is correct, not 2.
Mistake 4
Confusing the square root symbol with the cube root
Students need to be taught the difference between cube root and square root constantly as this will help them avoid mistakes.
For example: √(1/100) and ∛(1/100) are different.
Mistake 5
Misunderstanding the concept of perfect squares
Understanding which numbers are perfect squares is crucial.
For example, 100 is a perfect square because it is 10^2, so 1/100 is also a perfect square since it can be expressed as (1/10)^2.
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.
