122 LearnersLast updated on May 26th, 2025
Square Root of 801
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 various fields, including vehicle design, finance, etc. Here, we will discuss the square root of 801.
What is the Square Root of 801?
The square root is the inverse of the square of a number. 801 is not a perfect square. The square root of 801 is expressed in both radical and exponential forms. In radical form, it is expressed as √801, whereas in exponential form it is (801)^(1/2). √801 ≈ 28.3019, 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 801
The prime factorization method is used for perfect square numbers. However, for non-perfect square numbers, the long-division method and approximation method are used. Let us now learn the following methods:
- Prime factorization method
- Long division method
- Approximation method
Square Root of 801 by Prime Factorization Method
The product of prime factors is the prime factorization of a number. Now let us look at how 801 is broken down into its prime factors.
Step 1: Finding the prime factors of 801 Breaking it down, we get 3 x 3 x 89: 3^2 x 89^1
Step 2: Now we found the prime factors of 801. The second step is to make pairs of those prime factors. Since 801 is not a perfect square, the digits of the number can’t be grouped in pairs.
Therefore, calculating 801 using prime factorization does not give an exact integer result.
Square Root of 801 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 801, we need to group it as 01 and 8.
Step 2: Now we need to find a number n whose square is less than or equal to 8. We choose n = 2 because 2 x 2 = 4, which is less than 8. The quotient is 2, and the remainder is 4 after subtracting 4 from 8.
Step 3: Bring down the next pair, which is 01, making the new dividend 401.
Step 4: Double the quotient (2), giving us 4, and use it to find a new divisor. Consider 4n as the new divisor, and find n such that 4n x n ≤ 401.
Step 5: By trial, we find that n = 7 works, since 47 x 7 = 329.
Step 6: Subtract 329 from 401 to get a remainder of 72, and the quotient becomes 27.
Step 7: Since the dividend is less than the divisor, we need to add a decimal point. Adding a decimal point allows us to add two zeroes to the dividend, making it 7200.
Step 8: Find a new divisor by considering 54 (double the new quotient 27) and find n such that 54n x n ≤ 7200. With n = 1, 541 x 1 = 541.
Step 9: Subtract 541 from 7200 to get a remainder of 6659.
Step 10: The quotient is now approximately 28.301. Continue with these steps until you get the desired precision.
So the square root of √801 ≈ 28.3019.
Square Root of 801 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 801 using the approximation method.
Step 1: Find the closest perfect squares to √801.
The smallest perfect square less than 801 is 784 (28^2), and the largest perfect square greater than 801 is 841 (29^2). √801 falls somewhere between 28 and 29.
Step 2: Apply the formula: (Given number - smallest perfect square) / (Larger perfect square - smallest perfect square).
Using the formula: (801 - 784) / (841 - 784) = 17 / 57 ≈ 0.2982. Adding the value to the smaller perfect square root: 28 + 0.2982 = 28.2982, so the square root of 801 is approximately 28.3019.
Common Mistakes and How to Avoid Them in the Square Root of 801
Students often make mistakes while finding square roots, such as forgetting about the negative square root or skipping steps in the long division method. Let us look at a few common mistakes in detail.
Mistake 1
Forgetting about the negative square root
Students should remember that a number has both positive and negative square roots. However, we usually take only the positive square root, as it is the one most commonly used.
For example, √801 ≈ 28.3019, but there is also -28.3019.
Mistake 2
Not adding the square root symbol in proper places
Misplacing the square root symbol is a common mistake. Students should be taught to simplify expressions under the square root correctly.
For example, √(9 + 16) ≠ √9 + √16. The correct expression is √(9 + 16) = √25 = 5.
Mistake 3
Not finding the correct value of a non-perfect square
Students should first simplify expressions under the square root before approximating.
For example, √801 ≈ 28.3019, not 28 or 29.
Mistake 4
Confusing the square root symbol with the cube root
Students should be taught the difference between cube roots and square roots.
For example, √801 and ∛801 are different.
Mistake 5
Making mistakes in long division
The long division method involves many steps, and students might skip a step accidentally, leading to a wrong answer. It is important to practice this method carefully.
Square Root of 801 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √801?
The area of the square is approximately 801 square units.
Explanation
The area of a square = side^2.
The side length is given as √801.
Area of the square = side^2 = √801 x √801 = 801.
Therefore, the area of the square box is approximately 801 square units.
Problem 2
A square-shaped building measuring 801 square feet is built; if each of the sides is √801, what will be the square feet of half of the building?
400.5 square feet
Explanation
We can just divide the given area by 2 as the building is square-shaped.
Dividing 801 by 2 = we get 400.5.
So half of the building measures 400.5 square feet.
Problem 3
Calculate √801 x 5.
141.5095
Explanation
The first step is to find the square root of 801, which is approximately 28.3019.
The second step is to multiply 28.3019 by 5.
So, 28.3019 x 5 ≈ 141.5095.
Problem 4
What will be the square root of (784 + 17)?
The square root is approximately 28.3019.
Explanation
To find the square root, we need to find the sum of (784 + 17). 784 + 17 = 801, and the square root of 801 is approximately 28.3019.
Therefore, the square root of (784 + 17) is approximately ±28.3019.
Problem 5
Find the perimeter of the rectangle if its length ‘l’ is √801 units and the width ‘w’ is 38 units.
The perimeter of the rectangle is approximately 132.6038 units.
Explanation
Perimeter of the rectangle = 2 × (length + width).
Perimeter = 2 × (√801 + 38) = 2 × (28.3019 + 38) ≈ 2 × 66.3019 = 132.6038 units.
FAQ on Square Root of 801
1.What is √801 in its simplest form?
2.Mention the factors of 801.
3.Calculate the square of 801.
4.Is 801 a prime number?
5.801 is divisible by?
6.How does learning Algebra help students in United Arab Emirates make better decisions in daily life?
7.How can cultural or local activities in United Arab Emirates support learning Algebra topics such as Square Root of 801?
8.How do technology and digital tools in United Arab Emirates support learning Algebra and Square Root of 801?
9.Does learning Algebra support future career opportunities for students in United Arab Emirates?
Important Glossaries for the Square Root of 801
- Square root: A square root is the inverse of a square. Example: 5^2 = 25, and the inverse of the square is the square root, that is √25 = 5.
- 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.
- Principal square root: A number has both positive and negative square roots, but the positive square root is often used in real-world applications. This is known as the principal square root.
- Prime factorization: The expression of a number as the product of its prime factors. For example, the prime factorization of 801 is 3 x 3 x 89.
- Long division method: A method used for finding the square root of non-perfect squares by dividing and using successive approximations.
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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.
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