124 LearnersLast updated on May 26th, 2025
Square Root of 796
If a number is multiplied by itself, the result is a square. The inverse of squaring a number is finding its square root. Square roots are used in fields like architecture, finance, and physics. Here, we will discuss the square root of 796.
What is the Square Root of 796?
The square root is the inverse operation of squaring a number. 796 is not a perfect square. The square root of 796 is expressed in both radical and exponential form. In the radical form, it is expressed as √796, whereas in exponential form, it is (796)^(1/2). √796 ≈ 28.215, which is an irrational number as it cannot be expressed as a simple fraction.
Finding the Square Root of 796
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 these methods:
- Prime factorization method
- Long division method
- Approximation method
Square Root of 796 by Prime Factorization Method
The product of prime factors is the prime factorization of a number. Now let us look at how 796 is broken down into its prime factors.
Step 1: Finding the prime factors of 796 Breaking it down, we get 2 x 2 x 199. Since 199 is a prime number, 796 is expressed as 2² x 199.
Step 2: Now, we found out the prime factors of 796. Since 796 is not a perfect square, the digits of the number can’t be grouped into pairs, making it impossible to calculate the square root using prime factorization alone.
Square Root of 796 by Long Division Method
The long division method is particularly used for non-perfect square numbers. In this method, we try to find the closest perfect square number for the given number. Let us 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 796, we need to group it as 96 and 7.
Step 2: Now we need to find a number whose square is less than or equal to 7. We can take 2, as 2 x 2 = 4, which is less than 7. Now the quotient is 2. Subtracting 4 from 7 gives 3.
Step 3: Bring down 96 next to 3, making the new dividend 396. Double the previous quotient (2) to get 4, which will start our new divisor.
Step 4: Find a number, say n, such that 4n × n ≤ 396. We find n = 7 works because 47 x 7 = 329.
Step 5: Subtract 329 from 396 to get 67, and the quotient is now 27.
Step 6: Since the dividend is less than the divisor, we need to add a decimal point, which allows us to add two zeroes to the dividend. The new dividend is 6700.
Step 7: Find the next digit n such that (540 + n) × n ≤ 6700. We find n = 1 works because 541 x 1 = 541.
Step 8: Subtract 541 from 6700 to get 6159, and the quotient is now 28.1.
Step 9: Continue this process until the desired precision after the decimal is achieved.
So the square root of √796 is approximately 28.215.
Square Root of 796 by Approximation Method
The approximation method is another way to find 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 796 using the approximation method.
Step 1: Find the closest perfect squares around 796.
The smallest perfect square less than 796 is 784 (which is 28²), and the largest perfect square greater than 796 is 841 (which is 29²). √796 falls between 28 and 29.
Step 2: Now apply the formula: (Given number - smallest perfect square) / (Greater perfect square - smallest perfect square) (796 - 784) / (841 - 784) = 12 / 57 ≈ 0.21
Add this to the base square root value of 28 to get approximately 28.21.
Common Mistakes and How to Avoid Them in the Square Root of 796
Students often make mistakes while finding square roots, such as ignoring the negative square root or skipping steps in the long division method. Let's look at common mistakes in detail.
Mistake 1
Forgetting about the negative square root
It's important to remember that a number has both positive and negative square roots. However, we often use only the positive square root, as it is typically the required one.
For example: √49 = ±7, but the negative root is often overlooked.
Mistake 2
Not adding the square root symbol in the correct places
Incorrect use of the square root symbol is a common mistake. Students should simplify the numbers inside the square root before moving on.
For example: √(25 + 9) ≠ √25 + √9. The correct usage is √(25 + 9) = √34.
Mistake 3
Not finding the correct value of a non-perfect square
The first step is to simplify the numbers inside the square root to avoid mistakes in identifying the approximate value.
For example: √48 ≈ 6.928, not 7.
Mistake 4
Confusing the square root symbol with the cube root
Students need to understand the difference between square roots and cube roots.
For example, √64 is not the same as ∛64. The former is 8, while the latter is 4.
Mistake 5
Making mistakes in long division
Finding a square root using the long division method involves many steps. Students often skip a step accidentally, leading to incorrect answers. Careful attention is needed throughout the process.
Square root of 796 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √796?
The area of the square is 796 square units.
Explanation
The area of the square = side².
The side length is given as √796.
Area of the square = side² = √796 x √796 = 796.
Therefore, the area of the square box is 796 square units.
Problem 2
A square-shaped building measuring 796 square feet is built; if each of the sides is √796, what will be the square feet of half of the building?
398 square feet
Explanation
We divide the given area by 2 as the building is square-shaped.
Dividing 796 by 2, we get 398.
So half of the building measures 398 square feet.
Problem 3
Calculate √796 x 5.
141.075
Explanation
First, find the square root of 796, approximately 28.215.
Then multiply 28.215 by 5.
So 28.215 x 5 = 141.075.
Problem 4
What will be the square root of (796 + 4)?
The square root is 28.3.
Explanation
To find the square root, first find the sum of (796 + 4). 796 + 4 = 800, and then √800 ≈ 28.3.
Therefore, the square root of (796 + 4) is approximately ±28.3.
Problem 5
Find the perimeter of the rectangle if its length ‘l’ is √796 units and the width ‘w’ is 50 units.
We find the perimeter of the rectangle as 156.43 units.
Explanation
Perimeter of the rectangle = 2 × (length + width)
Perimeter = 2 × (√796 + 50) = 2 × (28.215 + 50) = 2 × 78.215 = 156.43 units.
FAQ on Square Root of 796
1.What is √796 in its simplest form?
2.Mention the factors of 796.
3.Calculate the square of 796.
4.Is 796 a prime number?
5.796 is divisible by?
6.How does learning Algebra help students in Philippines make better decisions in daily life?
7.How can cultural or local activities in Philippines support learning Algebra topics such as Square Root of 796?
8.How do technology and digital tools in Philippines support learning Algebra and Square Root of 796?
9.Does learning Algebra support future career opportunities for students in Philippines?
Important Glossaries for the Square Root of 796
- Square root: A square root is the inverse of squaring a number. For example, 5² = 25, and the inverse is √25 = 5.
- Irrational number: An irrational number cannot be expressed as a simple fraction. For example, the square root of a non-perfect square is irrational.
- Radical form: A way to express roots, such as square roots, using the radical symbol (√).
- Exponential form: A mathematical notation indicating repeated multiplication, such as expressing roots as fractional exponents, e.g., x^(1/2).
- Perfect square: A number that is the square of an integer, such as 1, 4, 9, 16, etc.
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Jaskaran Singh Saluja
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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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