126 LearnersLast updated on May 26th, 2025
Square Root of 64/4
If a number is multiplied by itself, the result is a square. The inverse operation of finding a square is finding a square root. Square roots are used in various fields such as engineering, finance, and science. Here, we will discuss the square root of 64/4.
What is the Square Root of 64/4?
The square root is the inverse of squaring a number. The number 64/4 simplifies to 16, which is a perfect square. The square root of 16 can be expressed in both radical and exponential form. In radical form, it is expressed as √16, whereas in exponential form, it is expressed as (16)^(1/2). The square root of 16 is 4, which is a rational number because it can be expressed as a fraction of two integers, such as 4/1.
Finding the Square Root of 64/4
For perfect square numbers, the prime factorization method can be used. Since 16 is a perfect square, we will explore the methods to find its square root:
- Prime factorization method
- Long division method
- Approximation method
Square Root of 64/4 by Prime Factorization Method
The prime factorization of a number involves expressing it as a product of prime numbers. Let's look at how 16 is broken down into its prime factors:
Step 1: Find the prime factors of 16.
Breaking it down, we get 2 × 2 × 2 × 2, which is 2^4.
Step 2: Make pairs of these prime factors. Since 16 is a perfect square, the digits can be grouped into pairs of two: (2 × 2) × (2 × 2).
Step 3: Take one number from each pair and multiply them: 2 × 2 = 4. Thus, the square root of 16 is 4.
Square Root of 64/4 by Long Division Method
The long division method can also be used for perfect square numbers. Here's how to find the square root using this method, step by step:
Step 1: Group the digits of 16 from right to left. In this case, it is just 16.
Step 2: Find the largest number whose square is less than or equal to 16. This number is 4, as 4 × 4 = 16.
Step 3: Subtract 16 from 16, leaving a remainder of 0. Since there is no remainder, the square root of 16 is 4.
Square Root of 64/4 by Approximation Method
The approximation method can be used for finding square roots, especially for non-perfect squares, but here it confirms the known result.
Step 1: Identify perfect squares closest to 16. The perfect squares 9 (3^2) and 16 (4^2) surround 16.
Step 2: Since 16 is already a perfect square, no further approximation is needed. The square root of 16 is confirmed as 4.
Common Mistakes and How to Avoid Them in the Square Root of 64/4
Mistakes can occur when finding square roots, such as forgetting about the negative square root, skipping steps in the long division method, or incorrectly simplifying numbers. Let's explore some common mistakes and how to avoid them.
Mistake 1
Forgetting about the negative square root
A number has both positive and negative square roots. When asked for the square root, unless specified otherwise, the positive root is usually required.
For example, √16 = 4, but there is also -4.
Mistake 2
Not adding the square root symbol in proper places
Incorrect usage of the square root symbol can lead to errors. Teach students to simplify numbers inside the square root before proceeding.
For example, √(4 + 12) = √16 = 4, not √4 + √12.
Mistake 3
Confusing between square roots and other roots
Students may confuse square roots with cube roots or other roots.
For example, √16 and ∛16 are different; the former is 4, while the latter is not a whole number.
Mistake 4
Errors in prime factorization
Errors can occur in identifying prime factors. Ensure students verify each factor is prime, like 2 × 2 × 2 × 2 for 16, leading to the correct square root of 4.
Mistake 5
Mistakes in long division
Finding a square root using long division involves several steps. Students may skip steps, leading to incorrect answers. Ensure each step is followed accurately, especially subtraction and finding the quotient.
Square Root of 64/4 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √64/4?
The area of the square is 16 square units.
Explanation
The area of a square = side^2.
The side length is given as √64/4, which simplifies to √16 = 4.
Area of the square = side^2 = 4 × 4 = 16.
Therefore, the area of the square box is 16 square units.
Problem 2
A square-shaped building measuring 64 square feet is built; if each of the sides is √64/4, what will be the square feet of half of the building?
32 square feet
Explanation
The total area of the building is 64 square feet.
Dividing 64 by 2 gives us 32.
So, half of the building measures 32 square feet.
Problem 3
Calculate √64/4 × 5.
20
Explanation
First, find the square root of 64/4, which simplifies to √16 = 4.
Then multiply 4 by 5: 4 × 5 = 20.
Problem 4
What will be the square root of (64/4 + 36)?
The square root is 8.
Explanation
First, find the sum of (64/4 + 36), which is 16 + 36 = 52.
The square root of 52 is approximately 7.211, but since 52 is not a perfect square, it cannot be simplified further.
Therefore, the square root of (64/4 + 36) is approximately 7.211.
Problem 5
Find the perimeter of the rectangle if its length 'l' is √64/4 units and the width 'w' is 10 units.
The perimeter of the rectangle is 28 units.
Explanation
Perimeter of the rectangle = 2 × (length + width).
Here, length = √64/4 = 4 and width = 10.
Perimeter = 2 × (4 + 10) = 2 × 14 = 28 units.
FAQ on Square Root of 64/4
1.What is √64/4 in its simplest form?
2.Mention the factors of 16.
3.Calculate the square of 64/4.
4.Is 16 a prime number?
5.16 is divisible by?
6.How does learning Algebra help students in Qatar make better decisions in daily life?
7.How can cultural or local activities in Qatar support learning Algebra topics such as Square Root of 64/4?
8.How do technology and digital tools in Qatar support learning Algebra and Square Root of 64/4?
9.Does learning Algebra support future career opportunities for students in Qatar?
Important Glossaries for the Square Root of 64/4
- Square Root: A square root is the inverse operation of squaring a number. For example, 4^2 = 16, and the inverse is √16 = 4.
- Perfect Square: A perfect square is an integer that is the square of an integer. For example, 16 is a perfect square because it is 4 squared.
- Rational Number: A rational number can be expressed as a fraction of two integers, such as 4/1 for the number 4.
- Prime Factorization: The process of breaking down a number into its prime factors. For example, 16 = 2 × 2 × 2 × 2.
- Perimeter: The total distance around a two-dimensional shape. For example, the perimeter of a rectangle is 2 × (length + width).
Explore More algebra
About BrightChamps in Qatar
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.
