Square Root of 14.4
2026-02-28 10:48 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-14.4

410 Learners

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 fields such as vehicle design, finance, etc. Here, we will discuss the square root of 14.4.

What is the Square Root of 14.4?

The square root is the inverse of the square of a number. 14.4 is not a perfect square. The square root of 14.4 is expressed in both radical and exponential form. In the radical form, it is expressed as √14.4, whereas (14.4)^(1/2) is the exponential form. √14.4 ≈ 3.79473, 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 14.4

The prime factorization method is used for perfect square numbers. However, the prime factorization method is not typically used for non-perfect square numbers, where methods such as 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 14.4 by Prime Factorization Method

The product of prime factors is the prime factorization of a number. Now, let us look at how 14.4 can be expressed in terms of its prime factors.

Step 1: Converting 14.4 into a fraction: 14.4 = 144/10 = (12 x 12)/(2 x 5).

Step 2: The prime factorization of 144 is 2 x 2 x 2 x 2 x 3 x 3. The prime factorization of 10 is 2 x 5.

Step 3: Now, we pair the prime factors of the numerator. Since 14.4 is not a perfect square, calculating √14.4 using prime factorization directly involves approximations.

Explore Our Programs

Square Root of 14.4 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 to 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 digits in pairs from right to left. In the case of 14.4, consider it as 1440 after multiplying by 100 for ease.

Step 2: Find an integer whose square is less than or equal to 14. Consider n = 3 because 3 x 3 = 9, which is less than 14.

Step 3: Subtract 9 from 14, giving a remainder of 5. Bring down the next pair, making it 540.

Step 4: Double the current quotient (3) to get 6, and use it as the base for the next divisor.

Step 5: Find a digit x such that 6x x x is less than or equal to 540. Using trial, x = 8 works because 68 x 8 = 544.

Step 6: Subtract 544 from 540, resulting in -4, so adjust x to 7, where 67 x 7 = 469.

Step 7: Continue the process to find the quotient to the desired decimal places.

The approximate square root is 3.79473.

Square Root of 14.4 by Approximation Method

The approximation method is another method for finding square roots; it is an easy method to approximate the square root of a given number. Let us learn how to find the square root of 14.4 using the approximation method.

Step 1: Identify the closest perfect squares around 14.4.

The closest smaller perfect square is 9 (√9 = 3), and the closest larger perfect square is 16 (√16 = 4).

Step 2: Using interpolation, approximate between these values: (14.4 - 9) / (16 - 9) = (14.4 - 9) / 7 = 0.7714

Step 3: Approximate the square root: 3 + 0.7714 = 3.7714

Thus, √14.4 ≈ 3.79473 using a more precise calculation.

Common Mistakes and How to Avoid Them in the Square Root of 14.4

Students often make mistakes while finding the square root, such as forgetting about the negative square root or skipping steps in the long division method. Let us look at a few of these mistakes in detail.

Problem 1

Can you help Max find the area of a square box if its side length is given as √14.4?

Okay, lets begin

The area of the square is approximately 14.4 square units.

Explanation

The area of a square = side².

The side length is given as √14.4.

Area of the square = (√14.4)² = 14.4.

Therefore, the area of the square box is approximately 14.4 square units.

Well explained 👍

Problem 2

A square-shaped field measures 14.4 square meters. What is the length of each side of the field?

Okay, lets begin

Each side of the field is approximately 3.79473 meters.

Explanation

The side length of a square is the square root of its area. √14.4 ≈ 3.79473.

Therefore, each side of the field is approximately 3.79473 meters.

Well explained 👍

Problem 3

Calculate √14.4 x 5.

Okay, lets begin

The result is approximately 18.97365.

Explanation

First, find the square root of 14.4, which is approximately 3.79473.

Then, multiply 3.79473 by 5: 3.79473 x 5 ≈ 18.97365.

Well explained 👍

Problem 4

What will be the square root of (14 + 0.4)?

Okay, lets begin

The square root is approximately 3.79473.

Explanation

To find the square root, calculate the sum: 14 + 0.4 = 14.4.

Then, √14.4 ≈ 3.79473.

Therefore, the square root of (14 + 0.4) is approximately 3.79473.

Well explained 👍

Problem 5

Find the perimeter of a rectangle if its length ‘l’ is √14.4 units and the width ‘w’ is 10 units.

Okay, lets begin

The perimeter of the rectangle is approximately 27.58946 units.

Explanation

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

Perimeter = 2 × (√14.4 + 10) ≈ 2 × (3.79473 + 10) ≈ 2 × 13.79473 ≈ 27.58946 units.

Well explained 👍

FAQ on Square Root of 14.4

1.What is √14.4 in its simplest form?

The square root of 14.4 is an irrational number and cannot be simplified to a simpler radical form. It is approximately 3.79473.

2.Calculate the square of 14.4.

The square of 14.4 is found by multiplying the number by itself: 14.4 x 14.4 = 207.36.

3.Is 14.4 a perfect square?

14.4 is not a perfect square, as it does not have an integer as its square root.

4.Is 14.4 a rational number?

Yes, 14.4 is a rational number because it can be expressed as a fraction: 144/10.

5.What is the square root of 14.4 approximated to two decimal places?

The square root of 14.4 approximated to two decimal places is 3.79.

Important Glossaries for the Square Root of 14.4

  • Square root: A square root is the inverse of squaring a number. For example, 4² = 16, and the inverse, the square root, is √16 = 4
     
  • Irrational number: An irrational number cannot be expressed as a fraction p/q, where q is not zero and p and q are integers.
     
  • Approximation: The process of finding a value close to the true value, often used when the exact value is difficult to find.
     
  • Long division method: A technique used to find the square root of a non-perfect square number through a series of division steps.
     
  • Decimal: A numerical representation that includes a whole number and a fractional part, separated by a decimal point, such as 7.86.

What Is Algebra? 🧮 | Simple Explanation with 🎯 Cool Examples for Kids | ✨BrightCHAMPS Math

▶

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.