Square Root of 15/16
2026-02-28 06:12 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-15/16

258 Learners

Last updated on August 5, 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.

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.

Explore Our Programs

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.

Problem 1

Can you help Max find the area of a square box if its side length is given as √(15/16)?

Okay, lets begin

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.

Well explained 👍

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?

Okay, lets begin

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.

Well explained 👍

Problem 3

Calculate √(15/16) × 5.

Okay, lets begin

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.

Well explained 👍

Problem 4

What will be the square root of (15/16 + 1/16)?

Okay, lets begin

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.

Well explained 👍

Problem 5

Find the perimeter of the rectangle if its length ‘l’ is √(15/16) units and the width ‘w’ is 2 units.

Okay, lets begin

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.

Well explained 👍

FAQ on Square Root of 15/16

1.What is √(15/16) in its simplest form?

The simplest form of √(15/16) is √15/4 since 15/16 is already in its simplest fractional form.

2.Mention the factors of 15/16.

The factors of the fraction 15/16 are not applicable as fractions do not have factors in the traditional sense, but 15 and 16 have factors. The factors of 15 are 1, 3, 5, and 15. The factors of 16 are 1, 2, 4, 8, and 16.

3.Calculate the square of 15/16.

We get the square of 15/16 by multiplying the number by itself, that is (15/16) × (15/16) = 225/256.

4.Is 15/16 a prime number?

5.15/16 is divisible by?

As a fraction, 15/16 does not have divisors in the traditional sense, but it can be expressed in decimal form and divided by numbers like any other decimal.

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.

What Is Algebra? 🧮 | Simple Explanation with 🎯 Cool Examples for Kids | ✨BrightCHAMPS Math

▶

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.