Last updated on May 26th, 2025
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.
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.
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:
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.
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.
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.
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.
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.
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.
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.
Calculate √(15/16) × 5.
Approximately 4.8555.
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.
What will be the square root of (15/16 + 1/16)?
The square root is 1.
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.
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.
Perimeter of the rectangle = 2 × (length + width). Perimeter = 2 × (√(15/16) + 2) ≈ 2 × (0.9711 + 2) ≈ 2 × 2.9711 ≈ 5.9422 units.
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.
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