120 LearnersLast updated on May 26th, 2025
Square Root of 808
If a number is multiplied by itself, the result is a square. The inverse of squaring is finding the square root. The square root is used in fields like engineering, finance, and more. Here, we will discuss the square root of 808.
What is the Square Root of 808?
The square root is the inverse operation of squaring a number. 808 is not a perfect square. The square root of 808 can be expressed in both radical and exponential forms. In radical form, it is expressed as √808, whereas in exponential form it is expressed as (808)^(1/2). √808 ≈ 28.414, which is an irrational number because it cannot be expressed as a simple fraction p/q, where p and q are integers and q ≠ 0.
Finding the Square Root of 808
The prime factorization method is typically used for perfect squares. However, for non-perfect squares like 808, methods such as the long-division method and approximation method are used. Let's explore these methods:
- Prime factorization method
- Long division method
- Approximation method
Square Root of 808 by Prime Factorization Method
Prime factorization involves breaking a number down into its prime factors. Now, let's see how 808 is broken down:
Step 1: Finding the prime factors of 808 Breaking it down, we get 2 x 2 x 2 x 101: 2^3 x 101^1
Step 2: Now that we have the prime factors of 808, we attempt to make pairs of those prime factors. Since 808 is not a perfect square, pairing is not possible.
Therefore, calculating √808 using prime factorization alone isn't feasible.
Square Root of 808 by Long Division Method
The long division method is useful for non-perfect square numbers. Here’s how to use it for finding the square root step by step:
Step 1: To begin with, group the digits in pairs from right to left. For 808, group it as 8 and 08.
Step 2: Find a number whose square is less than or equal to the first group (8). This number is 2, since 2^2 = 4. Subtract 4 from 8, leaving a remainder of 4.
Step 3: Bring down the next pair, 08, making the new dividend 408.
Step 4: Double the quotient obtained so far (2) to get 4. This becomes part of the new divisor.
Step 5: Find a digit n such that 4n × n is less than or equal to 408. The correct n is 6, since 46 × 6 = 276.
Step 6: Subtract 276 from 408, leaving a remainder of 132.
Step 7: Since the dividend is less than the divisor, add a decimal point and bring down 00, making it 13200.
Step 8: The new divisor becomes 566 (46 with an added digit 6), and the next digit in the quotient is 2. Thus, 562 × 2 = 1124.
Step 9: Subtract 1124 from 13200, resulting in 1176.
Step 10: Repeat these steps to refine the quotient. Eventually, the square root of 808 is approximately 28.41.
Square Root of 808 by Approximation Method
The approximation method is another way to estimate square roots. Here's how to approximate √808:
Step 1: Identify the closest perfect squares around 808. The nearest perfect squares are 784 (28^2) and 841 (29^2). So, √808 is between 28 and 29.
Step 2: Use the approximation formula: (Given number - smaller perfect square) / (larger perfect square - smaller perfect square). For 808, this is (808 - 784) / (841 - 784) = 24 / 57 ≈ 0.42.
Step 3: Add this to the smaller root: 28 + 0.42 = 28.42. So, the approximate square root of 808 is 28.42.
Common Mistakes and How to Avoid Them in the Square Root of 808
Students often make errors when finding square roots, such as forgetting about negative roots or misapplying methods. Let's examine some common mistakes:
Mistake 1
Forgetting about the negative square root
Students should remember that every positive number has both a positive and negative square root. However, in practical applications, the positive root is typically used.
For example, √25 = 5, but there is also -5.
Mistake 2
Not placing the square root symbol correctly
Incorrectly applying the square root symbol is a common mistake. It's crucial to simplify numbers inside the square root first.
For example, √(9 + 16) = √25 = 5, not √9 + √16 = 3 + 4.
Mistake 3
Misidentifying the value of a non-perfect square
When approximating square roots, students should simplify and carefully calculate.
For example, √50 ≈ 7.071, not 7.
Mistake 4
Confusing the square root with the cube root
Students often mix up square roots and cube roots. It's important to differentiate: √64 = 8, but ∛64 = 4.
Mistake 5
Errors in the long division method
The long division method has many steps, and skipping any can lead to errors. Patience and practice are key in ensuring accuracy.
Square Root of 808 Examples
Problem 1
Can you help Sam find the area of a square box if its side length is given as √128?
The area of the square is approximately 128.04 square units.
Explanation
The area of a square = side^2.
The side length is given as √128.
Area = (√128) × (√128) = 11.31 × 11.31 ≈ 128.04.
Therefore, the area of the square box is approximately 128.04 square units.
Problem 2
A square field measures 808 square feet. If each side is √808, what is the area of half the field?
404 square feet
Explanation
Since the field is square-shaped, dividing its area by 2 gives the area of half the field.
Dividing 808 by 2 yields 404.
Therefore, half of the field measures 404 square feet.
Problem 3
Calculate √808 x 4.
Approximately 113.656
Explanation
First, find the square root of 808, which is approximately 28.414.
Then multiply by 4.
So, 28.414 × 4 ≈ 113.656.
Problem 4
What is the square root of (808 + 32)?
The square root is 28.
Explanation
To find the square root, calculate (808 + 32) = 840. Since 841 is a perfect square (29^2), 840 is close enough to estimate the square root as approximately 28.97.
Therefore, the square root of (808 + 32) is approximately 28.97, which is about 28 for practical purposes.
Problem 5
Find the perimeter of a rectangle if its length 'l' is √808 units and the width 'w' is 20 units.
The perimeter of the rectangle is approximately 96.83 units.
Explanation
Perimeter of the rectangle = 2 × (length + width).
Perimeter = 2 × (√808 + 20) = 2 × (28.414 + 20) ≈ 2 × 48.414 ≈ 96.83 units.
FAQ on Square Root of 808
1.What is √808 in its simplest form?
2.What are the factors of 808?
3.Calculate the square of 808.
4.Is 808 a prime number?
5.808 is divisible by?
6.How does learning Algebra help students in Indonesia make better decisions in daily life?
7.How can cultural or local activities in Indonesia support learning Algebra topics such as Square Root of 808?
8.How do technology and digital tools in Indonesia support learning Algebra and Square Root of 808?
9.Does learning Algebra support future career opportunities for students in Indonesia?
Important Glossaries for the Square Root of 808
- Square root: The square root is an operation that finds a number which, when multiplied by itself, gives the original number. For example, √49 = 7.
- Irrational number: An irrational number is a number that cannot be expressed as a fraction of two integers. For example, √2 is irrational.
- Perfect square: A perfect square is a number that is the square of an integer. For example, 36 is a perfect square because it is 6^2.
- Long division method: A systematic method for finding square roots of non-perfect squares using division.
- Approximation method: A technique for estimating the square root of a number by finding nearby perfect squares and interpolating between them.
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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
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