Square Root of 1/16
2026-02-28 06:01 Diff
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Last updated on August 5, 2025

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.

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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.

Problem 1

Can you help Max find the area of a square box if its side length is given as √(1/16)?

Okay, lets begin

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.

Well explained 👍

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?

Okay, lets begin

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.

Well explained 👍

Problem 3

Calculate √(1/16) x 8.

Okay, lets begin

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.

Well explained 👍

Problem 4

What will be the square root of (1/16 + 15/16)?

Okay, lets begin

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.

Well explained 👍

Problem 5

Find the perimeter of a rectangle if its length ‘l’ is √(1/16) units and the width ‘w’ is 3 units.

Okay, lets begin

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.

Well explained 👍

FAQ on Square Root of 1/16

1.What is √(1/16) in its simplest form?

The prime factorization of 16 is 2 x 2 x 2 x 2, so the simplest form of √(1/16) = 1/4.

2.What are the factors of 1/16?

Factors of 1/16 in fractional form are 1/16 and 1, considering it as a number.

3.Calculate the square of 1/4.

We get the square of 1/4 by multiplying the number by itself, that is (1/4) x (1/4) = 1/16.

4.Is 1/16 a prime number?

5.Is 1/16 a rational number?

Yes, 1/16 is a rational number because it can be expressed as a fraction of integers.

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.