Square Root of 0.16
2026-02-28 09:45 Diff
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Last updated on August 5, 2025

If a number is multiplied by itself, the result is a square. The inverse of the square is a square root. The square root is used in various fields like vehicle design, finance, etc. Here, we will discuss the square root of 0.16.

What is the Square Root of 0.16?

The square root is the inverse of the square of the number. 0.16 is a perfect square. The square root of 0.16 is expressed in both radical and exponential forms. In the radical form, it is expressed as √0.16, whereas (0.16)^(1/2) in the exponential form. √0.16 = 0.4, 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 0.16

For perfect square numbers, methods like prime factorization are not typically needed because the square root can be calculated directly. However, for learning purposes, we can still explore methods like: Prime factorization method Long division method Approximation method

Square Root of 0.16 by Prime Factorization Method

The product of prime factors is the prime factorization of a number. Now let us look at how 0.16 is broken down into its prime factors:

Step 1: Express 0.16 as a fraction: 16/100.

Step 2: Find the prime factors of the numerator and denominator separately. 16 = 2 × 2 × 2 × 2 100 = 2 × 2 × 5 × 5

Step 3: Since 0.16 is a perfect square, we can pair the prime factors.

The result is (2/5)² = (0.4)², hence √0.16 = 0.4.

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Square Root of 0.16 by Long Division Method

The long division method is a systematic way to find the square root of non-perfect square numbers, but it can also be used for perfect squares for practice. Let us learn the steps:

Step 1: Consider 16 and 100 as integer equivalents (by multiplying by 100). We will find the square root of 16/100.

Step 2: Find a number whose square is less than or equal to 16. This number is 4 because 4 × 4 = 16.

Step 3: Since 16/100 is equivalent to 0.16, divide 4 by 10 to get 0.4.

Therefore, the square root of 0.16 is 0.4.

Square Root of 0.16 by Approximation Method

The approximation method is useful for non-perfect squares but can be applied to perfect squares as a learning tool.

Step 1: Identify the perfect squares closest to 0.16. Clearly, 0.16 itself is a perfect square.

Step 2: Since 0.16 = 0.4², the square root of 0.16 is exactly 0.4. Using this straightforward approach, we confirm that √0.16 = 0.4.

Common Mistakes and How to Avoid Them in the Square Root of 0.16

Students can make errors while finding square roots, such as ignoring the negative square root or misapplying methods. Let us look at some common mistakes in detail.

Problem 1

Can you help Max find the area of a square box if its side length is given as √0.25?

Okay, lets begin

The area of the square is 0.25 square units.

Explanation

The area of the square = side².

The side length is given as √0.25.

Area of the square = side²

= √0.25 × √0.25

= 0.5 × 0.5

= 0.25.

Therefore, the area of the square box is 0.25 square units.

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Problem 2

A square-shaped garden measures 0.16 square meters; if each of the sides is √0.16, what will be the square meters of half of the garden?

Okay, lets begin

0.08 square meters

Explanation

We can divide the given area by 2 as the garden is square-shaped.

Dividing 0.16 by 2 = we get 0.08.

So half of the garden measures 0.08 square meters.

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Problem 3

Calculate √0.16 × 10.

Okay, lets begin

4

Explanation

The first step is to find the square root of 0.16, which is 0.4.

The second step is to multiply 0.4 with 10. So 0.4 × 10 = 4.

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Problem 4

What will be the square root of (0.09 + 0.07)?

Okay, lets begin

The square root is 0.4

Explanation

To find the square root, we need to find the sum of (0.09 + 0.07). 0.09 + 0.07 = 0.16, and then √0.16 = 0.4. Therefore, the square root of (0.09 + 0.07) is ±0.4.

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Problem 5

Find the perimeter of the rectangle if its length 'l' is √0.16 units and the width 'w' is 0.24 units.

Okay, lets begin

We find the perimeter of the rectangle as 1.28 units.

Explanation

Perimeter of the rectangle = 2 × (length + width).

Perimeter = 2 × (√0.16 + 0.24)

= 2 × (0.4 + 0.24)

= 2 × 0.64

= 1.28 units.

Well explained 👍

FAQ on Square Root of 0.16

1.What is √0.16 in its simplest form?

The simplest form of √0.16 is 0.4.

2.What is the square of 0.4?

The square of 0.4 is 0.4 × 0.4 = 0.16.

3.Is 0.16 a perfect square?

Yes, 0.16 is a perfect square because √0.16 = 0.4, which is a rational number.

4.What are the factors of 0.16?

0.16 can be expressed as 16/100, and its factors include the factors of 16 (1, 2, 4, 8, 16) and 100 (1, 2, 4, 5, 10, 20, 25, 50, 100).

5.How do you express 0.16 as a fraction?

0.16 can be expressed as the fraction 16/100, which simplifies to 4/25.

Important Glossaries for the Square Root of 0.16

  • Square root: A square root is the inverse of a square. For example, 0.4² = 0.16 and the inverse of the square is the square root, that is, √0.16 = 0.4.
     
  • 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 has an integer as its square root. For example, 0.16 is a perfect square because √0.16 = 0.4.
     
  • Decimal: A decimal is a number that has a whole number and a fraction part separated by a decimal point. For example, 0.16 is a decimal.
     
  • Exponent: An exponent indicates the number of times a number is multiplied by itself. For example, in 0.16^(1/2), 1/2 is the exponent indicating the square root.

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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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: He loves to play the quiz with kids through algebra to make kids love it.