Square Root of 4.2
2026-02-28 17:21 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 4.2.

What is the Square Root of 4.2?

The square root is the inverse of the square of the number. 4.2 is not a perfect square. The square root of 4.2 is expressed in both radical and exponential form. In the radical form, it is expressed as √4.2, whereas (4.2)^(1/2) in the exponential form. √4.2 ≈ 2.04939, 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 4.2

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 4.2 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 group the numbers from right to left. In the case of 4.2, we need to consider it as 4.2.

Step 2: Now we need to find n whose square is closest to 4. We can say n is ‘2’ because 2 × 2 is equal to 4. Now the quotient is 2 after subtracting 4 from 4, the remainder is 0.

Step 3: Since we have a decimal, we bring down the next digit from the decimal part, which is 2, making the new dividend 20.

Step 4: Add the old divisor with the same number 2 + 2, we get 4, which will be our new divisor.

Step 5: The next step is finding 4n × n ≤ 20. Let's consider n as 0, now 4 × 0 × 0 = 0.

Step 6: Subtract 0 from 20, the difference is 20, and the quotient is 2.0.

Step 7: Since the dividend is larger than the divisor, we bring down another set of zeroes to continue the division process.

Step 8: Now we need to find the new divisor that fits the dividend. Repeat the steps to get more decimal places.

So the square root of √4.2 ≈ 2.04939.

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Square Root of 4.2 by Approximation Method

The approximation method is another method for finding the square roots, and it is an easy method to find the square root of a given number. Now let us learn how to find the square root of 4.2 using the approximation method.

Step 1: Now we have to find the closest perfect square of √4.2. The smallest perfect square less than 4.2 is 4, and the largest perfect square greater than 4.2 is 9. √4.2 falls somewhere between 2 and 3.

Step 2: Now we need to apply the formula that is: (Given number - smallest perfect square) / (Greater perfect square - smallest perfect square) Applying the formula: (4.2 - 4) / (9 - 4) = 0.2 / 5 = 0.04 Using the formula, we identified the decimal point of our square root. The next step is adding the value we got initially to the decimal number, which is 2 + 0.04 ≈ 2.04, so the square root of 4.2 is approximately 2.04939.

Common Mistakes and How to Avoid Them in the Square Root of 4.2

Students do make mistakes while finding the square root, like forgetting about the negative square root or skipping long division methods, 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 √4.2?

Okay, lets begin

The area of the square is approximately 17.64 square units.

Explanation

The area of the square = side².

The side length is given as √4.2.

Area of the square = side² = √4.2 × √4.2 ≈ 2.04939 × 2.04939 ≈ 4.2

Therefore, the area of the square box is approximately 4.2 square units.

Well explained 👍

Problem 2

A square-shaped building measuring 4.2 square feet is built; if each of the sides is √4.2, what will be the square feet of half of the building?

Okay, lets begin

2.1 square feet

Explanation

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

Dividing 4.2 by 2 = we get 2.1.

So half of the building measures 2.1 square feet.

Well explained 👍

Problem 3

Calculate √4.2 × 5.

Okay, lets begin

Approximately 10.24695

Explanation

The first step is to find the square root of 4.2, which is approximately 2.04939, the second step is to multiply 2.04939 with 5.

So 2.04939 × 5 ≈ 10.24695.

Well explained 👍

Problem 4

What will be the square root of (4.2 + 0.8)?

Okay, lets begin

The square root is approximately 2.236

Explanation

To find the square root, we need to find the sum of (4.2 + 0.8). 4.2 + 0.8 = 5, and then √5 ≈ 2.236.

Therefore, the square root of (4.2 + 0.8) is approximately ±2.236.

Well explained 👍

Problem 5

Find the perimeter of the rectangle if its length ‘l’ is √4.2 units and the width ‘w’ is 2 units.

Okay, lets begin

We find the perimeter of the rectangle as approximately 8.09878 units.

Explanation

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

Perimeter = 2 × (√4.2 + 2) = 2 × (2.04939 + 2) ≈ 2 × 4.04939 ≈ 8.09878 units.

Well explained 👍

FAQ on Square Root of 4.2

1.What is √4.2 in its simplest form?

Since 4.2 is not a perfect square, √4.2 cannot be simplified further in terms of integers. The approximate value is 2.04939.

2.Is 4.2 a perfect square?

No, 4.2 is not a perfect square because it cannot be expressed as the product of an integer with itself.

3.Calculate the square of 4.2.

We get the square of 4.2 by multiplying the number by itself, that is 4.2 × 4.2 = 17.64.

4.Is 4.2 a rational number?

5.Can √4.2 be expressed as a fraction?

No, √4.2 is an irrational number and cannot be expressed exactly as a fraction.

Important Glossaries for the Square Root of 4.2

  • Square root: A square root is the inverse of a square. Example: 4² = 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.
  • Principal square root: A number has both positive and negative square roots; however, it is always the positive square root that has more prominence due to its uses in the real world. That is the reason it is also known as the principal square root.
  • Rational number: A rational number is a number that can be expressed as the quotient or fraction p/q of two integers, where q is not zero.
  • Decimal: If a number has a whole number and a fraction in a single number, then it is called a decimal. For example: 4.2, 5.67, and 8.91 are decimals.

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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.