Square Root of 64/4
2026-02-28 06:07 Diff
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Last updated on August 5, 2025

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.

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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.

Problem 1

Can you help Max find the area of a square box if its side length is given as √64/4?

Okay, lets begin

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.

Well explained 👍

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?

Okay, lets begin

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.

Well explained 👍

Problem 3

Calculate √64/4 × 5.

Okay, lets begin

20

Explanation

First, find the square root of 64/4, which simplifies to √16 = 4.

Then multiply 4 by 5: 4 × 5 = 20.

Well explained 👍

Problem 4

What will be the square root of (64/4 + 36)?

Okay, lets begin

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.

Well explained 👍

Problem 5

Find the perimeter of the rectangle if its length 'l' is √64/4 units and the width 'w' is 10 units.

Okay, lets begin

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.

Well explained 👍

FAQ on Square Root of 64/4

1.What is √64/4 in its simplest form?

The simplest form of √64/4 is √16, which equals 4.

2.Mention the factors of 16.

Factors of 16 are 1, 2, 4, 8, and 16.

3.Calculate the square of 64/4.

The square of 64/4, which is 16, is 16 × 16 = 256.

4.Is 16 a prime number?

16 is not a prime number, as it has more than two factors.

5.16 is divisible by?

16 is divisible by 1, 2, 4, 8, and 16.

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).

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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.