107 LearnersLast updated on May 26th, 2025
Square Root of 1/16
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 1/16.
What is the Square Root of 1/16?
The square root is the inverse of the square of the number. 1/16 is a perfect square. The square root of 1/16 is expressed in both radical and exponential form. In the radical form, it is expressed as, √(1/16), whereas (1/16)^(1/2) in the exponential form. √(1/16) = 1/4, 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.
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Finding the Square Root of 1/16
The prime factorization method is used for perfect square numbers. The prime factorization method can be used for 1/16, as it is a perfect square. Here are the methods:
- Prime factorization method
- Simplification method
Square Root of 1/16 by Prime Factorization Method
The product of prime factors is the prime factorization of a number. Now let us look at how 1/16 is broken down into its prime factors.
Step 1: Finding the prime factors of 16 Breaking it down, we get 2 x 2 x 2 x 2: 2^4
Step 2: Now we found out the prime factors of 16. The second step is to make pairs of those prime factors. Since 16 is a perfect square, we can group the digits of the number in pairs. Therefore, √16 = 2 x 2 = 4.
Step 3: Since 1 is a perfect square, its square root is 1.
Step 4: Therefore, the square root of 1/16 is 1/4.
Square Root of 1/16 by Simplification Method
The simplification method can be used to find the square root of a fraction by taking the square root of the numerator and the denominator separately.
Step 1: Identify the numerator and the denominator of the fraction. For 1/16, the numerator is 1, and the denominator is 16.
Step 2: Find the square root of the numerator: √1 = 1.
Step 3: Find the square root of the denominator: √16 = 4.
Step 4: Divide the square root of the numerator by the square root of the denominator, giving 1/4.
Common Mistakes and How to Avoid Them in the Square Root of 1/16
Students do make mistakes while finding the square root, such as forgetting about the negative square root. Skipping simplification steps, etc. Now let us look at a few of those mistakes that students tend to make in detail.
Square Root of 1/16 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 = (1/4) x (1/4) = 1/16.
Therefore, the area of the square box is 1/16 square units.
Problem 2
A square-shaped garden measuring 1/16 square meters is built; if each of the sides is √(1/16), what will be the square meters of half of the garden?
1/32 square meters
Explanation
We can just divide the given area by 2 as the garden is square-shaped. Dividing 1/16 by 2 = 1/32. So half of the garden measures 1/32 square meters.
Problem 3
Calculate √(1/16) x 8.
2
Explanation
The first step is to find the square root of 1/16, which is 1/4. The second step is to multiply 1/4 with 8. So 1/4 x 8 = 2.
Problem 4
What will be the square root of (1/16 + 15/16)?
The square root is 1.
Explanation
To find the square root, we need to find the sum of (1/16 + 15/16).
1/16 + 15/16 = 1, and then √1 = 1.
Therefore, the square root of (1/16 + 15/16) is ±1.
Problem 5
Find the perimeter of a 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 × 3.25 = 6.5 units.
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FAQ on Square Root of 1/16
1.What is √(1/16) in its simplest form?
2.What are the factors of 1/16?
3.Calculate the square of 1/4.
4.Is 1/16 a prime number?
5.Is 1/16 a rational number?
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Important Glossaries for the Square Root of 1/16
- 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 number that is the square of an integer. Example: 16 is a perfect square because it is 4^2.
- Fraction: A mathematical expression representing the division of one integer by another. Example: 1/4, 3/8 are fractions.
- Simplification: The process of reducing a mathematical expression to its simplest form.
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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.
