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135 LearnersLast updated on December 15, 2025
Square Root of 80/5
If a number is multiplied by itself, the result is a square. The inverse of a square is a square root. Square roots are used in fields like vehicle design, finance, etc. Here, we will discuss the square root of 80/5.
What is the Square Root of 80/5?
The square root is the inverse of the square of a number. 80/5 simplifies to 16, which is a perfect square.
The square root of 80/5 is expressed in both radical and exponential form.
In radical form, it is expressed as √16, whereas (16)(1/2) in exponential form.
√16 = 4, which is a rational number because it can be expressed in the form of p/q, where p and q are integers and q ≠ 0.
Finding the Square Root of 80/5
The prime factorization method is used for perfect square numbers.
Since 16 is a perfect square, we can easily find its square root using the prime factorization method.
- Prime factorization method
- Long division method
- Approximation method
Square Root of 80/5 by Prime Factorization Method
The prime factorization of a number is the product of its prime factors.
Now, let us look at how 16 is broken down into its prime factors.
Step 1: Finding the prime factors of 16
Breaking it down, we get 2 x 2 x 2 x 2: 24
Step 2: Now that we have found the prime factors of 16, we can pair these factors. Since 16 is a perfect square, the pairs of prime factors can be grouped together.
Step 3: Take one factor from each pair: 2 x 2 = 4 Therefore, the square root of 16 is 4.
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Square Root of 80/5 by Long Division Method
The long division method is often used for non-perfect square numbers, but it can also be applied to perfect squares.
Let us learn how to find the square root using the long division method, step by step.
Step 1: Group the digits from right to left. In the case of 16, there is only one group: 16.
Step 2: Find a number whose square is less than or equal to 16. This number is 4 because 4 x 4 = 16.
Step 3: Subtract 16 from 16; the remainder is 0. Since there are no more groups to bring down, we are done. The quotient is 4, so the square root of 16 is 4.
Square Root of 80/5 by Approximation Method
The approximation method can be used to find square roots, though it is not necessary for perfect squares.
Let's see how this would work for 16.
Step 1: Identify the closest perfect squares to 16, which are 9 and 25.
Step 2: Since 16 is itself a perfect square, no further approximation is needed. The square root of 16 is precisely 4.
Common Mistakes and How to Avoid Them in the Square Root of 80/5
Students can make mistakes while finding the square root, such as forgetting about negative square roots or misapplying methods.
Let's explore some mistakes students make and how to avoid them.
Mistake 1
Forgetting about the negative square root
It's important to remind students that a number has both positive and negative square roots.
However, we usually consider only the positive square root for practical purposes.
For example, √16 = 4, and there is also -4, which should not be forgotten.
Mistake 2
Not adding the square root symbol in proper places
Incorrect usage of the square root symbol is another common mistake.
Teach students to simplify the numbers inside the square root before proceeding.
For example, √(4 + 12) = √16 is correct, not √4 + √12.
Mistake 3
Not finding the correct value of a non-perfect square
First, teach students to simplify the expression under the square root to avoid mistakes.
For example, √18 is not 6 but rather approximately 4.24.
Mistake 4
Confusing the square root symbol with the cube root
Students need to learn the difference between cube roots and square roots.
For example, √27 and โ27 are different.
Mistake 5
Making mistakes in long division
Finding a square root using the long division method involves many steps.
Students might skip steps accidentally, leading to errors.
This can happen in subtraction or elsewhere in the process.
Square Root of 80/5 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as โ64/4?
The area of the square is 16 square units.
Explanation
The area of a square = side2.
The side length is given as √64/4.
Area = (√64/4)2 = (8/4)2 = 22 = 4
Therefore, the area of the square box is 4 square units.
Problem 2
A square-shaped building measuring 80 square feet is built; if each of the sides is โ80/5, what will be the square feet of half of the building?
40 square feet
Explanation
We can divide the given area by 2 since the building is square-shaped.
Dividing 80 by 2, we get 40.
So half of the building measures 40 square feet.
Problem 3
Calculate โ80/5 x 5.
20
Explanation
First, find the square root of 80/5, which simplifies to √16 = 4.
Multiply 4 by 5.
So 4 x 5 = 20.
Problem 4
What will be the square root of (80/5 + 9)?
The square root is 5.
Explanation
To find the square root, we first find the sum of (80/5 + 9). 80/5 = 16, and 16 + 9 = 25. √25 = 5.
Therefore, the square root of (80/5 + 9) is 5.
Problem 5
Find the perimeter of a rectangle if its length 'l' is โ80/5 units and the width 'w' is 10 units.
The perimeter of the rectangle is 28 units.
Explanation
Perimeter of a rectangle = 2 × (length + width).
Perimeter = 2 × (√80/5 + 10) = 2 × (4 + 10) = 2 × 14 = 28 units.
FAQ on Square Root of 80/5
1.What is โ80/5 in its simplest form?
2.Mention the factors of 16.
3.Calculate the square of 16.
4.Is 16 a prime number?
5.16 is divisible by?
Important Glossaries for the Square Root of 80/5
- Square root: A square root is the inverse of a square. Example: 42 = 16 and the inverse of the square is the square root, that is, √16 = 4.
- Rational number: A rational number can be expressed in the form of p/q, where p and q are integers and q ≠ 0.
- Perfect square: A perfect square is a number that is the square of an integer. For example, 16 is a perfect square because it is 4^2.
- Prime factorization: Prime factorization is the process of writing a number as the product of its prime factors. For example, 16 = 2 x 2 x 2 x 2.
- Long division method: A method used to find the square root of a number by dividing and averaging. It is particularly useful for non-perfect squares but can be used for perfect squares as well.
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.
