Square Root of 3.2
2026-02-28 11:22 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-3.2

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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 various fields such as engineering, finance, and more. Here, we will discuss the square root of 3.2.

What is the Square Root of 3.2?

The square root is the inverse of the square of the number. 3.2 is not a perfect square. The square root of 3.2 is expressed in both radical and exponential form. In the radical form, it is expressed as √3.2, whereas (3.2)^(1/2) in the exponential form. √3.2 ≈ 1.78885, which is an irrational number because it cannot be expressed in the form of p/q, where p and q are integers and q ≠ 0.

Finding the Square Root of 3.2

The prime factorization method is used for perfect square numbers. However, the prime factorization method is not used for non-perfect square numbers, where the long-division method and approximation method are used. Let us now learn the following methods:

  • Prime factorization method
  • Long division method
  • Approximation method

Square Root of 3.2 by Prime Factorization Method

The product of prime factors is the prime factorization of a number. However, since 3.2 is not an integer, it cannot be broken down into prime factors using the traditional method applicable to whole numbers. Therefore, calculating the square root of 3.2 using prime factorization is not feasible.

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Square Root of 3.2 by Long Division Method

The long division method is particularly used for non-perfect square numbers. In this method, we should check the closest perfect square number for the given number. Let us now learn how to find the square root using the long division method, step by step:

Step 1: To begin with, we need to consider 3.2 as 32/10.

Step 2: Find the closest perfect square to 3.2. Here, the closest perfect square is 1.

Step 3: Divide and adjust using decimal places as needed.

Step 4: Continue the division process to gain precision, using decimal places to ensure accuracy.

Square Root of 3.2 by Approximation Method

The approximation method is another method for finding square roots and is an easy way to estimate the square root of a given number. Now let us learn how to find the square root of 3.2 using the approximation method.

Step 1: Now we have to find the closest perfect squares around 3.2. The closest perfect squares are 1 (1^2 = 1) and 4 (2^2 = 4). Thus, √3.2 falls between 1 and 2.

Step 2: Use interpolation to approximate more precisely if needed. Given that 3.2 is closer to 4 than to 1, we can estimate that √3.2 is approximately 1.78885.

Common Mistakes and How to Avoid Them in the Square Root of 3.2

Students often make mistakes while finding square roots, such as forgetting about the negative square root, skipping steps in the long division method, etc. Now let us look at a few of those mistakes in detail.

Problem 1

Can you help Max find the area of a square box if its side length is given as √3.2?

Okay, lets begin

The area of the square is approximately 3.2 square units.

Explanation

The area of a square = side^2.

The side length is given as √3.2.

Area of the square = (√3.2)^2 = 3.2.

Therefore, the area of the square box is approximately 3.2 square units.

Well explained 👍

Problem 2

A square-shaped garden measures 3.2 square meters in area. If each side is √3.2, what is the area of half of the garden?

Okay, lets begin

1.6 square meters

Explanation

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

Dividing 3.2 by 2 gives us 1.6.

So half of the garden measures 1.6 square meters.

Well explained 👍

Problem 3

Calculate √3.2 × 5.

Okay, lets begin

Approximately 8.94425

Explanation

First, find the square root of 3.2, which is approximately 1.78885.

Then multiply 1.78885 by 5.

So, 1.78885 × 5 ≈ 8.94425.

Well explained 👍

Problem 4

What will be the square root of (2.2 + 1)?

Okay, lets begin

The square root is approximately 2.

Explanation

To find the square root, first find the sum of 2.2 + 1 = 3.2.

Then, √3.2 ≈ 1.78885.

Therefore, the square root of (2.2 + 1) is approximately ±1.78885.

Well explained 👍

Problem 5

Find the perimeter of a rectangle if its length ‘l’ is √3.2 units and the width ‘w’ is 5 units.

Okay, lets begin

The perimeter of the rectangle is approximately 13.5777 units.

Explanation

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

Perimeter = 2 × (√3.2 + 5) ≈ 2 × (1.78885 + 5) ≈ 2 × 6.78885 ≈ 13.5777 units.

Well explained 👍

FAQ on Square Root of 3.2

1.What is √3.2 in its simplest form?

Since 3.2 is not a perfect square and cannot be expressed as a simple fraction, √3.2 is approximately 1.78885.

2.Is 3.2 a perfect square?

No, 3.2 is not a perfect square. It does not have an integer as its square root.

3.Calculate the square of 3.2.

We get the square of 3.2 by multiplying the number by itself, that is 3.2 × 3.2 = 10.24.

4.Is 3.2 a rational number?

Yes, 3.2 is a rational number because it can be expressed as a fraction, 32/10.

5.What are the closest whole numbers that √3.2 lies between?

√3.2 lies between 1 and 2 since 1^2 < 3.2 < 2^2.

Important Glossaries for the Square Root of 3.2

  • 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.
  • Irrational number: An irrational number is a number that cannot be written in the form of p/q, where q is not equal to zero and p and q are integers.
  • Rational number: A number that can be expressed as the quotient or fraction p/q of two integers, where q is not zero.
  • Decimal: A number that has a whole number and a fraction in a single number, such as 3.2 or 7.86.
  • Approximation: A value or number that is close to but not exactly equal to the actual value, often used when the exact value is difficult to obtain.

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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.