Square Root of 989

The square root is the inverse of the square of the number. 989 is not a perfect square. The square root of 989 is expressed in both radical and exponential form. In the radical form, it is expressed as √989, whereas (989)^(1/2) in the exponential form. √989 ≈ 31.446, 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.

For perfect square numbers, the prime factorization method is often used. However, for non-perfect square numbers like 989, the long division method and approximation method are more suitable. 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 989 is broken down into its prime factors: Step 1: Finding the prime factors of 989 Breaking it down, we get 23 × 43: 23^1 × 43^1 Step 2: Now that we have found the prime factors of 989, the second step is to make pairs of those prime factors. Since 989 is not a perfect square, the digits of the number cannot be grouped into pairs. Therefore, calculating 989 using prime factorization yields no exact square root.

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: Group the numbers from right to left. For 989, we group it as 89 and 9. Step 2: Find a number n whose square is less than or equal to 9. We can take n as 3 because 3 × 3 = 9. Now the quotient is 3, and after subtracting 9 - 9, the remainder is 0. Step 3: Bring down 89, which is the new dividend. Add the old divisor (3) with itself to get 6, which will be our new divisor. Step 4: Find a new n such that 6n × n ≤ 89. By checking, n=1 (61 × 1 = 61) fits the condition. Step 5: Subtract 61 from 89 to get the remainder 28, and the quotient is 31. Step 6: Add a decimal point, bring down 00 to make the new dividend 2800. Step 7: Now, find n such that 620n × n ≤ 2800. By trial, n=4 (620×4=2480) fits the condition. Step 8: Subtract 2480 from 2800 to get 320. Step 9: The quotient is 31.4. Continue the steps until you reach the desired precision. So the square root of √989 is approximately 31.446.

The approximation method is another method for finding square roots and provides a straightforward way to estimate the square root of a given number. Let's see how to find the square root of 989 using this method. Step 1: Find the closest perfect squares of √989. The closest perfect squares are 961 (31^2) and 1024 (32^2). Thus, √989 falls between 31 and 32. Step 2: Apply the formula: (Given number - smaller perfect square) / (larger perfect square - smaller perfect square) Using the formula: (989 - 961) / (1024 - 961) = 28 / 63 ≈ 0.444 Adding the value to the lower bound, we get 31 + 0.444 = 31.444, so the square root of 989 is approximately 31.444.

Square root: A square root is the inverse of a square. Example: 4^2 = 16, and the inverse of the square is the square root, so √16 = 4. Irrational number: An irrational number 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; however, the positive square root is typically used due to its common applications in the real world. This is known as the principal square root. Prime Factorization: Prime factorization is expressing a number as the product of its prime factors. Long Division Method: A method used to find the square root of a number by dividing it into groups of digits from right to left and using a series of steps to find the root.