Square Root of 5.2
2026-02-28 21:40 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 various fields such as physics, engineering, and finance. Here, we will discuss the square root of 5.2.

What is the Square Root of 5.2?

The square root is the inverse of the square of the number. 5.2 is not a perfect square. The square root of 5.2 is expressed in both radical and exponential form. In the radical form, it is expressed as √5.2, whereas (5.2)^(1/2) in the exponential form. √5.2 ≈ 2.28035, 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 5.2

For non-perfect square numbers like 5.2, methods such as the long-division method and approximation method are used to find the square root. Let us now learn the following methods:

  •  Long division method
  • Approximation method

Square Root of 5.2 by Long Division Method

The long division method is particularly used for non-perfect square numbers. This method provides a way to calculate the square root systematically. Here are the steps:

Step 1: Start by pairing the digits of 5.2 from the decimal point. Group as 5 and 20 (considering 5.2 as 5.20 for this method).

Step 2: Find a number whose square is less than or equal to 5. The closest number is 2 since 2^2 = 4.

Step 3: Write 2 in the quotient and subtract 4 from 5, giving a remainder of 1.

Step 4: Bring down 20 to make it 120. Double the quotient obtained (which is 2), giving 4, and use this to form the new divisor.

Step 5: Determine the next digit of the quotient by finding a number n such that 4n × n ≤ 120. The appropriate n is 2 since 42 × 2 = 84.

Step 6: Subtract 84 from 120, getting a remainder of 36. Continue this process by bringing down zeros and repeating the steps until the desired accuracy is reached.

The result is approximately 2.28035.

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Square Root of 5.2 by Approximation Method

The approximation method is an easy way to estimate the square root of a given number. Here's how to do it for 5.2:

Step 1: Identify the perfect squares closest to 5.2. These are 4 (2^2) and 9 (3^2).

Step 2: Since 5.2 is closer to 4 than to 9, start with the square root of 4, which is 2.

Step 3: Use linear approximation: (5.2 - 4) / (9 - 4) = 1.2 / 5 = 0.24.

Step 4: Add this decimal to the lower square root: 2 + 0.24 = 2.24

. Thus, the approximate square root of 5.2 is about 2.24.

Common Mistakes and How to Avoid Them in the Square Root of 5.2

Students often make mistakes while finding square roots, such as forgetting about the negative square root, misapplying methods, and more. Let's explore 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 √5.2?

Okay, lets begin

The area of the square is approximately 5.2 square units.

Explanation

The area of a square = side^2.

The side length is given as √5.2.

Area = (√5.2) × (√5.2) = 5.2.

Therefore, the area of the square box is approximately 5.2 square units.

Well explained 👍

Problem 2

A square-shaped building measuring approximately 5.2 square feet is built; if each of the sides is √5.2, what will be the square feet of half of the building?

Okay, lets begin

Approximately 2.6 square feet.

Explanation

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

Dividing 5.2 by 2 = 2.6.

So half of the building measures approximately 2.6 square feet.

Well explained 👍

Problem 3

Calculate √5.2 × 5.

Okay, lets begin

Approximately 11.40175.

Explanation

First, find the square root of 5.2, which is approximately 2.28035.

Then, multiply 2.28035 by 5.

So, 2.28035 × 5 ≈ 11.40175.

Well explained 👍

Problem 4

What will be the square root of (5 + 0.2)?

Okay, lets begin

Approximately 2.28035.

Explanation

To find the square root, calculate the sum of (5 + 0.2), which is 5.2. √5.2 ≈ 2.28035.

Therefore, the square root of (5 + 0.2) is approximately ±2.28035.

Well explained 👍

Problem 5

Find the perimeter of the rectangle if its length ‘l’ is √5.2 units and the width ‘w’ is 3 units.

Okay, lets begin

The perimeter of the rectangle is approximately 10.5607 units.

Explanation

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

Perimeter = 2 × (√5.2 + 3) = 2 × (2.28035 + 3) = 2 × 5.28035 = 10.5607 units.

Well explained 👍

FAQ on Square Root of 5.2

1.What is √5.2 in its simplest form?

The square root of 5.2 cannot be simplified further because 5.2 is not a perfect square. It is an irrational number approximately equal to 2.28035.

2.Is 5.2 a perfect square?

No, 5.2 is not a perfect square. A perfect square is a number that can be expressed as the square of an integer.

3.Calculate the square of 5.2.

The square of 5.2 is calculated by multiplying the number by itself, that is 5.2 × 5.2 = 27.04.

4.Is 5.2 a prime number?

5.What are the factors of 5.2?

5.2 is not an integer, so it does not have integer factors. However, in decimal form, you can consider its prime factors as 2 and 2.6.

Important Glossaries for the Square Root of 5.2

  • Square root: A square root of a number x is a number y such that y^2 = x. It is the inverse operation of squaring a number.
  • Irrational number: A number that cannot be expressed as a fraction a/b, where a and b are integers and b ≠ 0. Examples include √2, √3, and √5.2.
  • Principal square root: The non-negative square root of a number. For 5.2, this is approximately 2.28035.
  • Decimal: A number that has a whole part and a fractional part separated by a decimal point. For example, 5.2 is a decimal.
  • Long division method: A step-by-step process of dividing numbers to find the square root of non-perfect squares accurately.

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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.