102 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.
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.
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?
6.How does learning Algebra help students in United States make better decisions in daily life?
7.How can cultural or local activities in United States support learning Algebra topics such as Square Root of 1/16?
8.How do technology and digital tools in United States support learning Algebra and Square Root of 1/16?
9.Does learning Algebra support future career opportunities for students in United States?
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.
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