117 LearnersLast updated on May 26th, 2025
Square Root of 805
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 the field of vehicle design, finance, etc. Here, we will discuss the square root of 805.
What is the Square Root of 805?
The square root is the inverse of the square of the number. 805 is not a perfect square. The square root of 805 is expressed in both radical and exponential form. In the radical form, it is expressed as √805, whereas (805)^(1/2) in the exponential form. √805 ≈ 28.37252, 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 805
For perfect square numbers, the prime factorization method is used. However, for non-perfect square numbers like 805, the long-division method and approximation method are used. Let us now learn the following methods:
- Long division method
- Approximation method
Square Root of 805 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: Group the digits of 805 from right to left as 05 and 8.
Step 2: Find the greatest number whose square is less than or equal to the first group. For 8, that number is 2, because 2 x 2 = 4. The remainder is 8 - 4 = 4.
Step 3: Bring down the next group, making the new dividend 405. Double the quotient (2), and use it as part of the new divisor.
Step 4: Find a digit, say n, such that 4n x n is less than or equal to 405. Here, n is 8 because 48 x 8 = 384.
Step 5: Subtract 384 from 405 to get 21, and the quotient is 28.
Step 6: Since the remainder is less than the divisor, add a decimal point and bring down pairs of zeroes.
Step 7: Continue the process to get more decimal places as needed.
So the square root of √805 ≈ 28.37.
Square Root of 805 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. Let us learn how to find the square root of 805 using the approximation method.
Step 1: Identify the two closest perfect squares that 805 falls between. These are 784 (28^2) and 841 (29^2). Hence, √805 is between 28 and 29.
Step 2: Use the formula: (Given number - smaller perfect square) / (Larger perfect square - smaller perfect square). (805 - 784) / (841 - 784) ≈ 21 / 57 ≈ 0.368 Step 3: Add this decimal to the smaller square root: 28 + 0.368 ≈ 28.368.
So, the square root of 805 is approximately 28.368.
Common Mistakes and How to Avoid Them in the Square Root of 805
Students often make mistakes while finding the square root, such as forgetting about the negative square root or skipping steps in the long division method. Let's look at a few of these mistakes in detail.
Mistake 1
Forgetting about the negative square root
It is important to remember that a number has both positive and negative square roots. However, we usually take only the positive square root, as it is the required one in most practical applications.
For example, √50 = 7.07, but there is also -7.07, which should not be forgotten.
Mistake 2
Not adding the square root symbol in proper places
Not using the square root properly is another mistake that students make. To resolve this, students need to simplify the numbers inside the square root first.
For example, √(12 + 24) = √36, not √12 + √24.
Mistake 3
Not finding the correct value of a non-perfect square
The first step is to simplify the numbers inside the square root correctly. This ensures that students do not make mistakes while identifying the approximate value.
For example, √50 ≠ 7; the correct answer is √50 ≈ 7.071.
Mistake 4
Confusing the square root symbol with the cube root
Students need to be taught the difference between cube root and square root constantly.
For example, √50 and ∛50 are different.
Mistake 5
Making mistakes in long division
Finding a square root using the long division method involves many steps. Due to this, students might skip a step accidentally, resulting in a wrong answer at the end. This may occur during subtraction or elsewhere in the process.
Square root of 805 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √805?
The area of the square is approximately 805 square units.
Explanation
The area of the square = side^2.
The side length is given as √805.
Area of the square = (√805)^2 = 805.
Therefore, the area of the square box is approximately 805 square units.
Problem 2
A square-shaped building measuring 805 square feet is built; if each of the sides is √805, what will be the square feet of half of the building?
402.5 square feet
Explanation
We can divide the given area by 2 as the building is square-shaped.
Dividing 805 by 2 gives us 402.5.
So half of the building measures 402.5 square feet.
Problem 3
Calculate √805 x 5.
Approximately 141.86
Explanation
The first step is to find the square root of 805, which is approximately 28.37.
The second step is to multiply 28.37 by 5.
So, 28.37 x 5 ≈ 141.86.
Problem 4
What will be the square root of (805 + 36)?
The square root is approximately 29.
Explanation
To find the square root, we need to find the sum of (805 + 36). 805 + 36 = 841, and √841 = 29.
Therefore, the square root of (805 + 36) is ±29.
Problem 5
Find the perimeter of the rectangle if its length ‘l’ is √805 units and the width ‘w’ is 38 units.
The perimeter of the rectangle is approximately 132.74 units.
Explanation
Perimeter of the rectangle = 2 × (length + width).
Perimeter = 2 × (√805 + 38) ≈ 2 × (28.37 + 38) = 2 × 66.37 ≈ 132.74 units.
FAQ on Square Root of 805
1.What is √805 in its simplest form?
2.Mention the factors of 805.
3.Calculate the square of 805.
4.Is 805 a prime number?
5.805 is divisible by?
6.How does learning Algebra help students in Vietnam make better decisions in daily life?
7.How can cultural or local activities in Vietnam support learning Algebra topics such as Square Root of 805?
8.How do technology and digital tools in Vietnam support learning Algebra and Square Root of 805?
9.Does learning Algebra support future career opportunities for students in Vietnam?
Important Glossaries for the Square Root of 805
- Square root: A square root is the inverse of a square. Example: 4^2 = 16, and the inverse of the square is the square root, that is, √16 = 4.
- Irrational number: An irrational number is a number that cannot be written in the form of p/q, where q is not equal to zero and p and q are integers.
- Long division method: This is a method used to find the square root of non-perfect squares by dividing the number into groups and estimating digits step by step.
- Approximation method: A method for estimating the square root of a number by using nearby perfect squares to approximate the root.
- Perfect squares: Numbers that are the square of an integer. For example, 1, 4, 9, 16, etc., are perfect squares.
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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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