Square Root of 15/4
2026-02-28 06:16 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-15/4

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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 15/4.

What is the Square Root of 15/4?

The square root is the inverse of the square of the number. The fraction 15/4 is not a perfect square. The square root of 15/4 is expressed in both radical and exponential form. In the radical form, it is expressed as √(15/4), whereas (15/4)^(1/2) in the exponential form. √(15/4) = √15/2, 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 15/4

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 15/4 by Prime Factorization Method

The product of prime factors is the prime factorization of a number. Now let us look at how 15/4 is broken down into its prime factors.

Step 1: Finding the prime factors of 15 and 4. Breaking them down, we get 15 = 3 × 5 and 4 = 2 × 2.

Step 2: Now we found out the prime factors of 15 and 4. Since 15/4 is not a perfect square, we cannot pair the factors completely.

Therefore, calculating √(15/4) using prime factorization involves simplifying it to √15/2.

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Square Root of 15/4 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 numbers 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'll find the square root of the numerator 15 and the denominator 4 separately.

Step 2: The closest perfect square number to 15 is 16. The square root of 16 is 4, so √15 is slightly less than 4.

Step 3: For 4, the square root is 2.

Step 4: Therefore, √(15/4) = √15/2. Using the long division method or a calculator, √15 ≈ 3.87298.

Square Root of 15/4 by Approximation Method

The approximation method is another method for finding 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 15/4 using the approximation method.

Step 1: Now we have to find the closest perfect squares for the numerator 15, which are 9 and 16. √15 falls between 3 and 4.

Step 2: To approximate √15, we consider it as approximately 3.87298.

Step 3: Therefore, √(15/4) is approximately 3.87298/2 = 1.93649.

Common Mistakes and How to Avoid Them in the Square Root of 15/4

Students do make mistakes while finding the square root, like forgetting about the negative square root or skipping long division methods. 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 √(15/4)?

Okay, lets begin

The area of the square is 15/4 square units.

Explanation

The area of the square = side².

The side length is given as √(15/4).

Area of the square = (√(15/4))²

= 15/4.

Therefore, the area of the square box is 15/4 square units.

Well explained 👍

Problem 2

A square-shaped building measuring 15/4 square units is built; if each of the sides is √(15/4), what will be the square units of half of the building?

Okay, lets begin

15/8 square units

Explanation

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

Dividing 15/4 by 2 = 15/8.

So half of the building measures 15/8 square units.

Well explained 👍

Problem 3

Calculate √(15/4) × 5.

Okay, lets begin

9.68245

Explanation

The first step is to find the approximate square root of 15/4, which is 1.93649.

The second step is to multiply 1.93649 with 5.

So 1.93649 × 5 ≈ 9.68245.

Well explained 👍

Problem 4

What will be the square root of (15/4 + 1)?

Okay, lets begin

The square root is approximately 2.12132.

Explanation

To find the square root, we need to find the sum of (15/4 + 1).

15/4 + 1 = 19/4, and then √(19/4) = √19/2 ≈ 2.12132.

Therefore, the square root of (15/4 + 1) is approximately ±2.12132.

Well explained 👍

Problem 5

Find the perimeter of the rectangle if its length ‘l’ is √(15/4) units and the width ‘w’ is 2 units.

Okay, lets begin

The perimeter of the rectangle is approximately 7.87298 units.

Explanation

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

Perimeter = 2 × (√(15/4) + 2)

= 2 × (1.93649 + 2)

= 2 × 3.93649

= 7.87298 units.

Well explained 👍

FAQ on Square Root of 15/4

1.What is √(15/4) in its simplest form?

The prime factorization of 15 is 3 × 5, and 4 is 2 × 2, so the simplest form of √(15/4) = √15/2.

2.Mention the factors of 15 and 4.

Factors of 15 are 1, 3, 5, and 15. Factors of 4 are 1, 2, and 4.

3.Calculate the square of 15/4.

We get the square of 15/4 by multiplying the number by itself, that is (15/4) × (15/4) = 225/16.

4.Is 15/4 a prime fraction?

5.15/4 is divisible by?

15/4 is divisible by 1, 3/4, 5/4, and 15/4.

Important Glossaries for the Square Root of 15/4

  • 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, q is not equal to zero, and p and q are integers. Example: √2 ≈ 1.414.
     
  • Fraction: A fraction represents a part of a whole or, more generally, any number of equal parts. It is represented as p/q where p and q are integers and q ≠ 0.
     
  • Approximation: Approximating involves finding a value that is close enough to the right answer, usually within a specified range.
     
  • Prime factorization: Prime factorization is the process of breaking down a number into its basic prime number components.

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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.