Square Root of 283

The square root is the inverse of the square of the number. 283 is not a perfect square. The square root of 283 is expressed in both radical and exponential form. In the radical form, it is expressed as √283, whereas (283)^(1/2) in exponential form. √283 ≈ 16.8226, 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, the prime factorization method is not used for non-perfect square numbers, where long division and approximation methods are used. Let us now learn the following methods:

• Prime factorization method
• Long division method
• Approximation method

The product of prime factors is the prime factorization of a number. Now let us look at how 283 is broken down into its prime factors.

Step 1: Finding the prime factors of 283 283 is a prime number, so it cannot be broken down into smaller prime factors. Therefore, calculating 283 using prime factorization directly is not applicable.

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 283, we treat it as 283.

Step 2: Now we need to find n whose square is less than or equal to 2. We can say n as ‘1’ because 1×1 is less than or equal to 2. Now the quotient is 1, and after subtracting 1 from 2, the remainder is 1.

Step 3: Bring down 83 to make the new dividend 183. Double the quotient 1 to get 2, which becomes the start of the new divisor.

Step 4: Find a digit x such that 2x×x is less than or equal to 183. Here, 26×6 = 156.

Step 5: Subtract 156 from 183, and the remainder is 27.

Step 6: Since the remainder is less than the new divisor, add a decimal point to the quotient. Adding the decimal point allows us to add two zeroes to the dividend. The new dividend becomes 2700.

Step 7: Now, find a digit y such that 32y×y is less than or equal to 2700.

Step 8: Continue this process until you get sufficient decimal places.

So, the square root of √283 ≈ 16.82.

The approximation method is another way to find 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 283 using the approximation method.

Step 1: First, find the closest perfect square numbers around 283. The smallest perfect square less than 283 is 256, and the largest perfect square greater than 283 is 289. √283 falls between 16 and 17.

Step 2: Apply the formula: (Given number - smallest perfect square) / (Greater perfect square - smallest perfect square) Using the formula (283 - 256) / (289 - 256) = 27 / 33 ≈ 0.818 Adding this to the smaller square root gives us approximately 16.82.

• Square root: A square root is the inverse of squaring a number. Example: 4² = 16, and the inverse is the square root, so √16 = 4.

• Irrational number: An irrational number cannot be expressed as a fraction of two integers. It has a non-repeating, non-terminating decimal expansion.

• Principal square root: A number has both positive and negative square roots, but the positive square root is typically used in real-world applications and is known as the principal square root.

• Prime number: A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself.

• Approximation: The process of finding a value that is close enough to the correct answer, typically used when an exact answer is not necessary or possible.