Last updated on May 26th, 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.
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.
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:
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.
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.
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.
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.
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.
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.
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
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.
Calculate √64/4 × 5.
20
First, find the square root of 64/4, which simplifies to √16 = 4.
Then multiply 4 by 5: 4 × 5 = 20.
What will be the square root of (64/4 + 36)?
The square root is 8.
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.
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.
Perimeter of the rectangle = 2 × (length + width).
Here, length = √64/4 = 4 and width = 10.
Perimeter = 2 × (4 + 10) = 2 × 14 = 28 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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