121 LearnersLast updated on May 26th, 2025
Square Root of 802
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 such as engineering, finance, etc. Here, we will discuss the square root of 802.
What is the Square Root of 802?
The square root is the inverse of the square of the number. 802 is not a perfect square. The square root of 802 is expressed in both radical and exponential form. In the radical form, it is expressed as √802, whereas (802)^(1/2) in the exponential form. √802 ≈ 28.317, 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 802
The prime factorization method is used for perfect square numbers. However, for non-perfect square numbers, the prime factorization method is not used; instead, the long-division method and approximation method are used. Let's now learn the following methods:
- Prime factorization method
- Long division method
- Approximation method
Square Root of 802 by Prime Factorization Method
The product of prime factors is the prime factorization of a number. Now let us look at how 802 is broken down into its prime factors.
Step 1: Finding the prime factors of 802 Breaking it down, we get 2 x 401.
Step 2: Now we found out the prime factors of 802. The second step is to make pairs of those prime factors. Since 802 is not a perfect square, the digits of the number can’t be grouped in pairs.
Therefore, calculating √802 using prime factorization is not feasible.
Square Root of 802 by Long Division Method
The long division method is particularly used for non-perfect square numbers. In this method, we need to find 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 802, we need to group it as 02 and 8.
Step 2: Now we need to find n whose square is ≤ 8. We can say n is ‘2’ because 2 x 2 = 4, which is less than or equal to 8. Now the quotient is 2, and after subtracting 4 from 8, the remainder is 4.
Step 3: Now let us bring down 02, making the new dividend 402. Add the old divisor with the same number: 2 + 2 = 4, which will be our new divisor.
Step 4: The new divisor will be the sum of the dividend and quotient. Now we get 4n as the new divisor; we need to find the value of n.
Step 5: The next step is finding 4n × n ≤ 402. Let us consider n as 7; now 47 x 7 = 329.
Step 6: Subtract 329 from 402; the difference is 73, and the quotient is 27.
Step 7: Since the dividend is less than the divisor, we need to add a decimal point. Adding the decimal point allows us to add two zeroes to the dividend. Now the new dividend is 7300.
Step 8: Now we need to find the new divisor. Consider 549 because 549 x 9 = 4941.
Step 9: Subtracting 4941 from 7300, we get the result 2359.
Step 10: Now the quotient is 28.3.
Step 11: Continue doing these steps until we get two numbers after the decimal point. Suppose there are no decimal values; continue until the remainder is zero.
So the square root of √802 is approximately 28.31.
Square Root of 802 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 802 using the approximation method.
Step 1: Now we have to find the closest perfect square of √802.
The smallest perfect square less than 802 is 784, and the largest perfect square greater than 802 is 841. √802 falls somewhere between 28 and 29.
Step 2: Now we need to apply the formula: (Given number - smallest perfect square) / (Greater perfect square - smallest perfect square). Going by the formula: (802 - 784) ÷ (841 - 784) = 18/57 ≈ 0.316.
Using the formula, we identified the decimal point of our square root. The next step is adding the value we got initially to the decimal number, which is 28 + 0.316 ≈ 28.316.
Thus, the square root of 802 is approximately 28.316.
Common Mistakes and How to Avoid Them in the Square Root of 802
Students often make mistakes while finding the square root, such as forgetting about the negative square root, skipping steps in methods like the long division method, etc. Now let us look at a few of those mistakes that students tend to make 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 for 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 children make. To resolve this, we need to teach children that simplifying the numbers inside the square root is important and then move on to the second step.
For example: √(12 + 24) = √12 + √24 is incorrect. The right way is √(12 + 24) = √36.
Mistake 3
Not finding the correct value of a non-perfect square
The first step that needs to be taught to children is to approximate the numbers inside the square root. This is important so that students do not make mistakes while identifying the approximate value.
For example: √50 ≈ 7.071, not 7.
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 as this will help them avoid mistakes.
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, many students might skip a step accidentally, which results in a wrong answer at the end of the problem. This may either happen in subtraction or elsewhere.
Square root of 802 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √802?
The area of the square is approximately 802 square units.
Explanation
The area of the square = side².
The side length is given as √802.
Area of the square = side² = √802 × √802 = 802.
Therefore, the area of the square box is approximately 802 square units.
Problem 2
A square-shaped building measuring 802 square feet is built. If each of the sides is √802, what will be the square feet of half of the building?
401 square feet
Explanation
We can divide the given area by 2 as the building is square-shaped.
Dividing 802 by 2 = 401.
So half of the building measures 401 square feet.
Problem 3
Calculate √802 × 5.
141.585
Explanation
The first step is to find the square root of 802, which is approximately 28.317.
The second step is to multiply 28.317 by 5.
So 28.317 × 5 ≈ 141.585.
Problem 4
What will be the square root of (782 + 20)?
The square root is approximately 28.317.
Explanation
To find the square root, we need to find the sum of (782 + 20). 782 + 20 = 802, and then the square root of 802 is approximately 28.317.
Therefore, the square root of (782 + 20) is ±28.317.
Problem 5
Find the perimeter of the rectangle if its length ‘l’ is √802 units and the width ‘w’ is 38 units.
The perimeter of the rectangle is approximately 132.634 units.
Explanation
Perimeter of the rectangle = 2 × (length + width).
Perimeter = 2 × (√802 + 38) = 2 × (28.317 + 38) = 2 × 66.317 ≈ 132.634 units.
FAQ on Square Root of 802
1.What is √802 in its simplest form?
2.Mention the factors of 802.
3.Calculate the square of 802.
4.Is 802 a prime number?
5.802 is divisible by?
6.How does learning Algebra help students in Australia make better decisions in daily life?
7.How can cultural or local activities in Australia support learning Algebra topics such as Square Root of 802?
8.How do technology and digital tools in Australia support learning Algebra and Square Root of 802?
9.Does learning Algebra support future career opportunities for students in Australia?
Important Glossaries for the Square Root of 802
- 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.
- 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: A method used to find the square root of a non-perfect square number using division and subtraction.
- Approximation method: A method used to estimate the square root by comparing it with nearby perfect squares. Perfect square: A number that is the square of an integer. For example, 9 is a perfect square as it is 3².
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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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