107 LearnersLast updated on May 26th, 2025
Square Root of 8.5
If a number is multiplied by the same number, the result is a square. The inverse of the square is a square root. The square root is used in fields like architecture, physics, and finance, among others. Here, we will discuss the square root of 8.5.
What is the Square Root of 8.5?
The square root is the inverse of the square of the number. 8.5 is not a perfect square. The square root of 8.5 is expressed in both radical and exponential form. In the radical form, it is expressed as √8.5, whereas (8.5)^(1/2) in the exponential form. √8.5 ≈ 2.91548, 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 8.5
The prime factorization method is typically used for perfect square numbers. However, for non-perfect square numbers like 8.5, the long division method and approximation method are preferred. Let us now learn these methods: Long division method Approximation method
Square Root of 8.5 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 now learn how to find the square root using the long division method, step by step.
Step 1: To begin with, we need to group the numbers from right to left. In the case of 8.5, consider the number as 8.50.
Step 2: Now, find n whose square is less than or equal to 8. The number n is 2 because 2 x 2 = 4, which is less than or equal to 8. Now the quotient is 2.
Step 3: Subtract 4 from 8, and bring down 50 to make it 450.
Step 4: Double the quotient (2), which is now 4. We need to find a number x such that 4x multiplied by x is less than or equal to 450.
Step 5: The next step is finding the value of x. Let us consider x as 9, then 49 x 9 = 441.
Step 6: Subtract 441 from 450; the difference is 9.
Step 7: Since the remainder is not zero, add two zeroes to continue the division.
Step 8: Continue the process to get two numbers after the decimal point.
The square root of 8.5 is approximately 2.91.
Square Root of 8.5 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. Now let us learn how to find the square root of 8.5 using the approximation method.
Step 1: Find the closest perfect square of √8.5.
The closest perfect squares surrounding 8.5 are 4 and 9. √8.5 falls somewhere between 2 and 3.
Step 2: Now, apply the interpolation formula: (Given number - smallest perfect square) / (Greater perfect square - smallest perfect square)
Using the formula (8.5 - 4) / (9 - 4) = 0.9 Add the value we got initially to the base perfect square root, which is 2 + 0.9 = 2.9, so the square root of 8.5 is approximately 2.9.
Common Mistakes and How to Avoid Them in the Square Root of 8.5
Students often make mistakes while finding the square root, such as forgetting about the negative square root and skipping critical steps in the long division method. Let's discuss some common mistakes in detail.
Mistake 1
Forgetting about the negative square root
It is important to make students aware that a number has both positive and negative square roots. However, we typically consider only the positive square root, as it is often the required one.
For example, √8.5 ≈ 2.91; there is also -2.91, which should not be forgotten.
Square root of 8.5 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √8.5?
The area of the square is approximately 8.5 square units.
Explanation
The area of a square = side².
The side length is given as √8.5.
Area of the square = (√8.5)² = 8.5
Therefore, the area of the square box is approximately 8.5 square units.
Problem 2
A square-shaped garden measuring 8.5 square feet is built; if each of the sides is √8.5, what will be the square feet of half of the garden?
4.25 square feet
Explanation
We can divide the given area by 2 since the garden is square-shaped.
Dividing 8.5 by 2 = 4.25
So half of the garden measures 4.25 square feet.
Problem 3
Calculate √8.5 × 10.
Approximately 29.15
Explanation
First, find the square root of 8.5, which is approximately 2.915.
Then multiply 2.915 by 10. So, 2.915 × 10 ≈ 29.15
Problem 4
What will be the square root of (8 + 0.5)?
Approximately 2.91
Explanation
To find the square root, calculate the sum of (8 + 0.5). 8 + 0.5 = 8.5, and then √8.5 ≈ 2.91.
Therefore, the square root of (8 + 0.5) is approximately ±2.91.
Problem 5
Find the perimeter of the rectangle if its length ‘l’ is √8.5 units and the width ‘w’ is 3 units.
Approximately 11.83 units
Explanation
Perimeter of the rectangle = 2 × (length + width)
Perimeter = 2 × (√8.5 + 3) ≈ 2 × (2.915 + 3) ≈ 2 × 5.915 ≈ 11.83 units.
FAQ on Square Root of 8.5
1.What is √8.5 in its simplest form?
2.Mention the factors of 8.5.
3.Calculate the square of 8.5.
4.Is 8.5 a prime number?
5.8.5 is divisible by?
6.How does learning Algebra help students in Bahrain make better decisions in daily life?
7.How can cultural or local activities in Bahrain support learning Algebra topics such as Square Root of 8.5?
8.How do technology and digital tools in Bahrain support learning Algebra and Square Root of 8.5?
9.Does learning Algebra support future career opportunities for students in Bahrain?
Important Glossaries for the Square Root of 8.5
- Square root: The square root of a number is a value that, when multiplied by itself, gives the original number. For example, the square root of 9 is 3 because 3 × 3 = 9.
- Irrational number: An irrational number cannot be expressed as a simple fraction, meaning it cannot be written as a ratio of two integers.
- Principal square root: This refers to the non-negative square root of a number. For example, the principal square root of 8.5 is approximately 2.915.
- Decimal: A decimal is a number that contains a whole number part and a fractional part separated by a decimal point. For example, 8.5 is a decimal.
- Approximation: This refers to a value or quantity that is nearly but not exactly correct; it is often used when calculating irrational numbers like square roots.
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About BrightChamps in Bahrain
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.
