116 LearnersLast updated on May 26th, 2025
Square Root of 15/2
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 15/2.
What is the Square Root of 15/2?
The square root is the inverse of the square of the number. 15/2 is not a perfect square. The square root of 15/2 is expressed in both radical and exponential form. In the radical form, it is expressed as, √(15/2), whereas (15/2)^(1/2) in the exponential form. √(15/2) = 1.93649, 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 15/2
The prime factorization method is used for perfect square numbers. However, for non-perfect square numbers, 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 15/2 by Prime Factorization Method
The product of prime factors is the prime factorization of a number. For the fraction 15/2, we will find the prime factors of the numerator and the denominator separately.
Step 1: Finding the prime factors of 15 and 2 Breaking it down, we get 15 = 3 x 5 and 2 = 2. So the prime factorization of 15/2 is 3 x 5 / 2.
Step 2: Since 15/2 is not a perfect square, calculating √(15/2) using prime factorization directly is not possible, but understanding the factorization helps in other methods.
Square Root of 15/2 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. Here is how to find the square root using the long division method, step by step.
Step 1: To begin with, express 15/2 as a decimal, which is 7.5.
Step 2: Now, group the number 7.5 from right to left. For this, consider it as 7.50.
Step 3: Find n such that n^2 is less than or equal to 7. The nearest perfect square is 4 (2 x 2), so n is 2. Subtract 4 from 7 to get 3, and bring down 50 to make it 350.
Step 4: Double the divisor (2) to make it 4. Find the largest digit "d" such that 4d x d is less than or equal to 350. The result is 46 x 6 = 276.
Step 5: Subtract 276 from 350 to get 74, and bring down two zeros to make it 7400.
Step 6: Continue this process to get the square root to desired decimal places.
So the square root of √(15/2) is approximately 1.936.
Square Root of 15/2 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 15/2 using the approximation method.
Step 1: Convert 15/2 to a decimal, which is 7.5.
Step 2: Find the closest perfect squares around 7.5. The nearest perfect squares are 4 (2^2) and 9 (3^2). √(7.5) falls between 2 and 3.
Step 3: Apply the approximation formula: (Given number - smaller perfect square) / (larger perfect square - smaller perfect square). Using the formula, (7.5 - 4) / (9 - 4) = 0.7.
Step 4: Add the initial whole number, 2 + 0.7 = 2.7. Since this is an approximation to the nearest whole number, refine it to get a more accurate result. Thus, the square root of 15/2 is approximately 1.936.
Common Mistakes and How to Avoid Them in the Square Root of 15/2
Students often make mistakes while finding the square root, such as forgetting about the negative square root or skipping necessary steps in methods like long division. Let's look at a few mistakes in detail.
Mistake 1
Forgetting about the negative square root
It is important to remember that a number has both positive and negative square roots. However, we usually consider only the positive square root for practical applications.
For example, √50 = 7.07, but there is also -7.07, which should not be forgotten.
Mistake 2
Not adding square root symbols in proper places
Not using the square root symbol properly is a common mistake. Ensure simplification of numbers inside the square root before proceeding.
For example, √(12+24) = √36, not √12 + √24.
Mistake 3
Not finding the correct value of a non-perfect square
The first step is to simplify numbers inside the square root to avoid errors in identifying approximate values.
For instance, √50 = 7 is incorrect; the correct value is √50 ≈ 7.071067.
Mistake 4
Confusing the square root symbol with the cube root
Teach students the difference between cube roots and square roots to prevent this mistake.
For example, √50 and ∛50 are different.
Mistake 5
Making mistakes in long division
Finding a square root using the long division method involves many steps. Students might skip a step accidentally, resulting in incorrect answers. This may occur during subtraction or other steps.
Square root of 15/2 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √(15/2)?
The area of the square is approximately 7.5 square units.
Explanation
The area of the square = side^2.
The side length is given as √(15/2).
Area of the square = side^2 = √(15/2) x √(15/2) = 15/2 = 7.5.
Therefore, the area of the square box is approximately 7.5 square units.
Problem 2
A square-shaped building measuring 15/2 square feet is built; if each of the sides is √(15/2), what will be the square feet of half of the building?
3.75 square feet.
Explanation
We can just divide the given area by 2 as the building is square-shaped.
Dividing 15/2 by 2 = we get 15/4 = 3.75.
So half of the building measures 3.75 square feet.
Problem 3
Calculate √(15/2) x 5.
9.68245
Explanation
The first step is to find the square root of 15/2, which is approximately 1.93649.
The second step is to multiply 1.93649 by 5.
So 1.93649 x 5 ≈ 9.68245.
Problem 4
What will be the square root of (15/2 + 1)?
The square root is approximately 2.121.
Explanation
To find the square root, first find the sum of (15/2 + 1).
15/2 + 1 = 15/2 + 2/2 = 17/2 = 8.5.
The square root of 8.5 is approximately 2.915.
Therefore, the square root of (15/2 + 1) is approximately 2.915.
Problem 5
Find the perimeter of the rectangle if its length ‘l’ is √(15/2) units and the width ‘w’ is 5 units.
We find the perimeter of the rectangle as approximately 13.873 units.
Explanation
Perimeter of the rectangle = 2 × (length + width).
Perimeter = 2 × (√(15/2) + 5) ≈ 2 × (1.93649 + 5) ≈ 2 × 6.93649 ≈ 13.873 units.
FAQ on Square Root of 15/2
1.What is √(15/2) in its simplest form?
2.Mention the factors of 15/2.
3.Calculate the square of 15/2.
4.Is 15/2 a prime number?
5.15/2 is divisible by?
Important Glossaries for the Square Root of 15/2
- Square root: A square root is the inverse of a square. For example, 4^2 = 16 and the inverse of the square is the square root, that is, √16 = 4.
- Irrational number: An irrational number cannot be written in the form of p/q, where q is not equal to zero and p and q are integers.
- Fraction: A fraction consists of a numerator and a denominator, such as 15/2, where 15 is the numerator and 2 is the denominator.
- Decimal: If a number has a whole number and a fraction in a single number, it is called a decimal. For example, 7.86, 8.65, and 9.42 are decimals.
- Approximation: Approximating means finding a value that is close to the actual value. Often used when exact values are not feasible, especially with irrational numbers.
Explore More algebra
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.
