104 LearnersLast updated on May 26th, 2025
Square Root of 15/4
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.
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.
Mistake 1
Forgetting about the negative square root
It is important to make students aware that a number does have both positive and negative square roots. However, we typically consider only the positive square root, as it is the required one.
For example: √4 = 2, but there is also -2, which should not be forgotten.
Square Root of 15/4 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √(15/4)?
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.
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?
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.
Problem 3
Calculate √(15/4) × 5.
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.
Problem 4
What will be the square root of (15/4 + 1)?
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.
Problem 5
Find the perimeter of the rectangle if its length ‘l’ is √(15/4) units and the width ‘w’ is 2 units.
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.
FAQ on Square Root of 15/4
1.What is √(15/4) in its simplest form?
2.Mention the factors of 15 and 4.
3.Calculate the square of 15/4.
4.Is 15/4 a prime fraction?
5.15/4 is divisible by?
6.How does learning Algebra help students in Singapore make better decisions in daily life?
7.How can cultural or local activities in Singapore support learning Algebra topics such as Square Root of 15/4?
8.How do technology and digital tools in Singapore support learning Algebra and Square Root of 15/4?
9.Does learning Algebra support future career opportunities for students in Singapore?
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.
