Square Root of 985

The square root is the inverse of the square of the number. 985 is not a perfect square. The square root of 985 is expressed in both radical and exponential form. In the radical form, it is expressed as √985, whereas (985)^(1/2) in the exponential form. √985 ≈ 31.3847, 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 method and approximation method 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 985 is broken down into its prime factors. Step 1: Finding the prime factors of 985. Breaking it down, we get 5 x 197. Since 985 is not a perfect square, the digits of the number can’t be grouped in pairs. Therefore, calculating √985 using prime factorization is not feasible.

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 985, we need to group it as 85 and 9. Step 2: Now we need to find n whose square is close to 9. We can say n is '3' because 3 x 3 = 9, which is equal to 9. Now the quotient is 3, and after subtracting 9 from 9, the remainder is 0. Step 3: Now let us bring down 85, which is the new dividend. Add the old divisor with the same number 3 + 3, we get 6, which will be our new divisor. Step 4: The new divisor will be 6n. We need to find the value of n such that 6n x n ≤ 85. Let us consider n as 1, now 6 x 1 x 1 = 61. Step 5: Subtract 61 from 85; the difference is 24, and the quotient is 31. Step 6: 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 2400. Step 7: Now we need to find the new divisor, which is 618 because 618 x 3 = 1854. Step 8: Subtracting 1854 from 2400, we get the result 546. Step 9: The quotient now is 31.38. Step 10: Continue doing these steps until we get two numbers after the decimal point. If there are no decimal values, continue until the remainder is zero. So the square root of √985 is approximately 31.38.

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 985 using the approximation method. Step 1: Now we have to find the closest perfect squares of √985. The smallest perfect square less than 985 is 961, and the largest perfect square greater than 985 is 1024. √985 falls somewhere between 31 and 32. Step 2: Now we need to apply the formula: (Given number - smallest perfect square) / (Greater perfect square - smallest perfect square). Going by the formula (985 - 961) / (1024 - 961) = 24/63 ≈ 0.38. 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 31 + 0.38 = 31.38, so the square root of 985 is approximately 31.38.

Square root: The 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. Principal square root: A number has both positive and negative square roots; however, it is always the positive square root that has more prominence due to its uses in the real world. This is the reason it is also known as a principal square root. Decimal: If a number has a whole number and a fraction in a single number, then it is called a decimal. For example, 7.86, 8.65, and 9.42 are decimals. Long division method: A method used to find square roots of non-perfect squares through division, providing an approximate value.