119 LearnersLast updated on May 26th, 2025
Square Root of 15/16
If a number is multiplied by itself, the result is a square. The inverse of the square is a square root. The square root is used in various fields including vehicle design, finance, etc. Here, we will discuss the square root of 15/16.
What is the Square Root of 15/16?
The square root is the inverse of the square of a number. 15/16 is not a perfect square. The square root of 15/16 is expressed in both radical and exponential form. In radical form, it is expressed as √(15/16), whereas (15/16)^(1/2) in exponential form. √(15/16) = √15/4, 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 15/16
The prime factorization method is used for perfect square numbers. However, for non-perfect square numbers like 15/16, the prime factorization method is not used. Instead, we use methods such as the long-division method and approximation method. Let us now learn the following methods:
- Long division method
- Approximation method
Square Root of 15/16 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 learn how to find the square root using the long division method, step by step.
Step 1: Convert the fraction 15/16 into decimal form, which is 0.9375.
Step 2: Find the closest perfect square numbers around 0.9375, which are 0.81 (√0.81 = 0.9) and 1 (√1 = 1).
Step 3: Use the long division method starting with the group, find the quotient whose square is less than or equal to 0.9375.
Step 4: The closest estimation is between 0.9 and 1.0.
Step 5: Continue the division process to find a more precise square root. The approximate square root is 0.9682.
Square Root of 15/16 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. Let us learn how to find the square root of 15/16 using the approximation method.
Step 1: Find the closest perfect squares of 15/16. The smallest perfect square is 0.81 and the largest is 1.
Step 2: Now apply the formula: (Given number - smallest perfect square) / (Greater perfect square - smallest perfect square). Using the formula: (0.9375 - 0.81) / (1 - 0.81) = 0.1275 / 0.19 ≈ 0.6711.
Step 3: Adding the value we got initially to the decimal number, which is 0.9 + 0.0711 = 0.9711. Hence, the square root of 15/16 is approximately 0.9711.
Common Mistakes and How to Avoid Them in the Square Root of 15/16
Students often make mistakes while finding the square root, such as forgetting about the negative square root, skipping long division steps, etc. Let us look at a few common 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 in practical applications.
For example: √(15/16) = 0.9711, but there is also -0.9711, which should not be forgotten.
Mistake 2
Not adding the square root symbol in proper places
Not using the square root symbol properly is a common mistake. It is important to simplify the numbers inside the square root first.
For example: √(9/16 + 6/16) = √(15/16) and not √(9/16) + √(6/16).
Mistake 3
Not finding the correct value of a non-perfect square
The first step in teaching is to simplify the numbers inside the square root to ensure they find the correct approximate value.
For example: √(25/36) = 5/6, not 25/36.
Mistake 4
Confusing the square root symbol with the cube root
Students need to understand the difference between cube root and square root to prevent mistakes.
For example: √(27/64) and ∛(27/64) are different.
Mistake 5
Making mistakes in the long division
Finding a square root using the long division method involves many steps. Students might skip steps accidentally, leading to incorrect answers. This can happen during subtraction or elsewhere in the process.
Square Root of 15/16 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √(15/16)?
The area of the square is approximately 0.9409 square units.
Explanation
The area of the square = side².
The side length is given as √(15/16).
Area of the square = side² = √(15/16) × √(15/16) ≈ 0.9711 × 0.9711 ≈ 0.9409.
Therefore, the area of the square box is approximately 0.9409 square units.
Problem 2
A square-shaped building measuring 15/16 square feet is built; if each of the sides is √(15/16), what will be the square feet of half of the building?
Approximately 0.46875 square feet.
Explanation
We can divide the given area by 2 as the building is square-shaped.
Dividing 15/16 by 2 = 15/32 ≈ 0.46875.
So half of the building measures approximately 0.46875 square feet.
Problem 3
Calculate √(15/16) × 5.
Approximately 4.8555.
Explanation
The first step is to find the square root of 15/16, which is approximately 0.9711.
The second step is to multiply 0.9711 by 5.
So 0.9711 × 5 ≈ 4.8555.
Problem 4
What will be the square root of (15/16 + 1/16)?
The square root is 1.
Explanation
To find the square root, we need to find the sum of (15/16 + 1/16). 15/16 + 1/16 = 1, and then √1 = 1. Therefore, the square root of (15/16 + 1/16) is 1.
Problem 5
Find the perimeter of the rectangle if its length ‘l’ is √(15/16) units and the width ‘w’ is 2 units.
We find the perimeter of the rectangle as approximately 5.9422 units.
Explanation
Perimeter of the rectangle = 2 × (length + width). Perimeter = 2 × (√(15/16) + 2) ≈ 2 × (0.9711 + 2) ≈ 2 × 2.9711 ≈ 5.9422 units.
FAQ on Square Root of 15/16
1.What is √(15/16) in its simplest form?
2.Mention the factors of 15/16.
3.Calculate the square of 15/16.
4.Is 15/16 a prime number?
5.15/16 is divisible by?
6.How does learning Algebra help students in Thailand make better decisions in daily life?
7.How can cultural or local activities in Thailand support learning Algebra topics such as Square Root of 15/16?
8.How do technology and digital tools in Thailand support learning Algebra and Square Root of 15/16?
9.Does learning Algebra support future career opportunities for students in Thailand?
Important Glossaries for the Square Root of 15/16
- Square root: A square root is the inverse of a square. For 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, where q is not equal to zero and p and q are integers.
- Principal square root: A number has both positive and negative square roots, but the positive square root is often used in real-world applications and is known as the principal square root.
- Decimal: A decimal is a number that includes a whole number and a fractional part, represented by a decimal point. For example: 0.9711.
- Fraction: A fraction represents a part of a whole or, more generally, any number of equal parts. It is expressed as a numerator divided by a denominator, such as 15/16.
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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.
