Square Root of 14.5
2026-02-28 09:16 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 fields such as vehicle design, finance, etc. Here, we will discuss the square root of 14.5.

What is the Square Root of 14.5?

The square root is the inverse of the square of the number. 14.5 is not a perfect square. The square root of 14.5 is expressed in both radical and exponential form. In the radical form, it is expressed as √14.5, whereas (14.5)^(1/2) in the exponential form. √14.5 ≈ 3.8079, 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 14.5

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 14.5 by Prime Factorization Method

The product of prime factors is the prime factorization of a number. However, since 14.5 is not a perfect square and is a decimal, the prime factorization method cannot be directly applied as it is with whole numbers.

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Square Root of 14.5 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: Group the numbers from right to left. For 14.5, it's already a single number.

Step 2: Identify a number n whose square is closest to 1. The closest perfect square is 1 (1×1), so the first digit of the quotient is 1.

Step 3: Subtract to get the remainder and bring down the decimal part to work with 450.

Step 4: Double the current quotient (1) to get 2, which will be used as the new divisor's first digit.

Step 5: Find a digit x such that 2x × x is less than or equal to 450. For x = 3, 23 × 3 = 69.

Step 6: Subtract 69 from 450 to get 381, and continue the process to get the decimal places.

Continue the steps until you achieve the desired precision, leading to an approximate square root of 3.8079.

Square Root of 14.5 by Approximation Method

The approximation method is another method for finding the square roots. 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 14.5 using the approximation method.

Step 1: Identify the closest perfect squares to √14.5. The closest perfect squares are 9 (3×3) and 16 (4×4), so √14.5 is between 3 and 4.

Step 2: Apply the formula: (Given number - smaller perfect square) / (larger perfect square - smaller perfect square).

Using the formula: (14.5 - 9) / (16 - 9) = 5.5 / 7 ≈ 0.7857

Adding this to the lower integer: 3 + 0.7857 ≈ 3.7857

So the square root of 14.5 is approximately 3.8079.

Common Mistakes and How to Avoid Them in the Square Root of 14.5

Students can make mistakes while finding the square root, such as forgetting about the negative square root. 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 √14.5?

Okay, lets begin

The area of the square is approximately 14.5 square units.

Explanation

The area of the square = side².

The side length is given as √14.5.

Area of the square = (√14.5)² = 14.5.

Therefore, the area of the square box is 14.5 square units.

Well explained 👍

Problem 2

A square-shaped garden measuring 14.5 square meters is built; if each of the sides is √14.5, what will be the square meters of half of the garden?

Okay, lets begin

7.25 square meters

Explanation

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

Dividing 14.5 by 2, we get 7.25.

So half of the garden measures 7.25 square meters.

Well explained 👍

Problem 3

Calculate √14.5 × 5.

Okay, lets begin

Approximately 19.04

Explanation

The first step is to find the square root of 14.5, which is approximately 3.8079.

The second step is to multiply 3.8079 by 5.

So 3.8079 × 5 ≈ 19.04.

Well explained 👍

Problem 4

What will be the square root of (14 + 0.5)?

Okay, lets begin

The square root is approximately 3.8079.

Explanation

To find the square root, we need to find the sum of (14 + 0.5), which is 14.5.

Then, √14.5 ≈ 3.8079.

Therefore, the square root of (14 + 0.5) is approximately ±3.8079.

Well explained 👍

Problem 5

Find the perimeter of the rectangle if its length ‘l’ is √14.5 units and the width ‘w’ is 4 units.

Okay, lets begin

We find the perimeter of the rectangle as approximately 15.62 units.

Explanation

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

Perimeter = 2 × (√14.5 + 4) = 2 × (3.8079 + 4) = 2 × 7.8079 ≈ 15.62 units.

Well explained 👍

FAQ on Square Root of 14.5

1.What is √14.5 in its simplest form?

Since 14.5 is not a perfect square, √14.5 is already in its simplest radical form: √14.5.

2.Is 14.5 a perfect square?

No, 14.5 is not a perfect square because its square root is not an integer.

3.Calculate the square of 14.5.

We get the square of 14.5 by multiplying the number by itself: 14.5 × 14.5 = 210.25.

4.Is 14.5 a prime number?

5.What are the factors of 14.5?

Since 14.5 is a decimal, it does not have factors in the same way that whole numbers do.

Important Glossaries for the Square Root of 14.5

  • Square root: A square root is the inverse of a square. Example: 4² = 16, and the inverse of the square is the square root, which 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.
     
  • Decimal: A decimal is a number that includes a fractional component, such as 7.86, 8.65, and 9.42.
     
  • Approximation: The process of finding a value that is close enough to the right answer, usually with some thought or calculation involved.
     
  • Long division method: A method used to find the square root of non-perfect squares by dividing the number into pairs and finding the most accurate quotient possible.

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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.