Last updated on May 26th, 2025
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 like vehicle design, finance, etc. Here, we will discuss the square root of 839.
The square root is the inverse of the square of the number. 839 is not a perfect square. The square root of 839 is expressed in both radical and exponential form. In the radical form, it is expressed as √839, whereas (839)^(1/2) in the exponential form. √839 ≈ 28.964, 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.
The prime factorization method is used for perfect square numbers. However, for non-perfect square numbers like 839, the long division method and approximation method are used. Let us now explore the following methods:
The product of prime factors is the prime factorization of a number. To find the prime factors of 839, we see that it is a prime number itself, so it cannot be broken down further into smaller prime factors. Therefore, calculating √839 using prime factorization involves recognizing it as a prime number, indicating that it does not simplify further into a product of smaller primes.
The long division method is particularly used for non-perfect square numbers. Here’s how to find the square root using the long division method, step by step:
Step 1: Group the numbers from right to left. For 839, it's grouped as 39 and 8.
Step 2: Find n whose square is less than or equal to 8. n is 2 because 2 × 2 = 4, which is less than 8. The quotient is 2, and the remainder is 8 - 4 = 4.
Step 3: Bring down the next pair, 39, making the new dividend 439. Double the previous quotient (2) to get 4, which will be the start of the new divisor.
Step 4: Find a digit x such that 4x × x ≤ 439. Here, x is 8 because 48 × 8 = 384, which is less than 439.
Step 5: Subtract 384 from 439, getting a remainder of 55.
Step 6: Add a decimal point and bring down two zeros, making the new dividend 5500.
Step 7: Double the quotient so far (28), making it 56. Find a digit y such that 56y × y ≤ 5500. Continue this process to get the decimal value.
Following these steps, we find the square root of 839 to be approximately 28.964.
The approximation method is another way to find square roots. Let's find the square root of 839 using this method:
Step 1: Identify the closest perfect squares around 839.
The nearest perfect squares are 841 (29²) and 784 (28²). Thus, √839 falls between 28 and 29.
Step 2: Use linear interpolation to approximate: (Given number - lower square) / (Upper square - lower square) (839 - 784) / (841 - 784) ≈ 0.964 Adding this to the lower boundary: 28 + 0.964 = 28.964
Therefore, the approximate square root of 839 is 28.964.
Students often make mistakes while finding the square root, such as forgetting about the negative square root, skipping steps in the long division method, etc. Let's discuss some common mistakes in detail.
Can you help Max find the area of a square box if its side length is given as √839?
The area of the square is 839 square units.
The area of a square = side².
The side length is given as √839.
Area = (√839)² = 839.
Therefore, the area of the square box is 839 square units.
A square-shaped building measuring 839 square feet is built; if each of the sides is √839, what will be the square feet of half of the building?
419.5 square feet
We can divide the given area by 2 since the building is square-shaped.
Dividing 839 by 2 gives us 419.5.
So, half of the building measures 419.5 square feet.
Calculate √839 × 5.
144.82
First, find the square root of 839, which is approximately 28.964.
Then multiply 28.964 by 5. 28.964 × 5 = 144.82
What will be the square root of (800 + 39)?
The square root is approximately 28.964.
First, find the sum: 800 + 39 = 839. The square root of 839 is approximately 28.964.
Find the perimeter of the rectangle if its length 'l' is √839 units and the width 'w' is 40 units.
The perimeter of the rectangle is approximately 137.928 units.
Perimeter of the rectangle = 2 × (length + width)
Perimeter = 2 × (√839 + 40) ≈ 2 × (28.964 + 40) Perimeter ≈ 2 × 68.964 = 137.928 units
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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