Square Root of 990

The square root is the inverse of the square of the number. 990 is not a perfect square. The square root of 990 is expressed in both radical and exponential form. In the radical form, it is expressed as √990, whereas (990)^(1/2) in the exponential form. √990 ≈ 31.4643, 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 typically used for perfect square numbers. However, for non-perfect squares like 990, 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 990 is broken down into its prime factors. Step 1: Finding the prime factors of 990 Breaking it down, we get 2 × 3 × 3 × 5 × 11: 2^1 × 3^2 × 5^1 × 11^1 Step 2: Now we found out the prime factors of 990. The second step is to make pairs of those prime factors. Since 990 is not a perfect square, the digits of the number can’t be grouped into pairs. Therefore, calculating 990 using prime factorization is impractical.

The long division method is particularly useful 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, group the numbers from right to left. In the case of 990, group it as 90 and 9. Step 2: Now find n whose square is less than or equal to 9. We choose n as '3' because 3 × 3 = 9. The quotient is 3, and after subtracting 9 - 9, the remainder is 0. Step 3: Bring down 90, which is the new dividend. Add the old divisor with the same number: 3 + 3 = 6, which will be our new divisor. Step 4: The new divisor will be the sum of the dividend and quotient. Now, we get 6n as the new divisor, and we need to find the value of n. Step 5: Find 6n × n ≤ 90. Let us consider n as 1; now 6 × 1 = 6. Step 6: Subtract 90 from 6 × 1. The difference is 84, and the quotient is 31. Step 7: Since the dividend is less than the divisor, add a decimal point. Adding the decimal point allows us to add two zeros to the dividend. The new dividend is 8400. Step 8: Find the new divisor, which is 62 because 624 × 4 = 2496. Step 9: Subtracting 2496 from 8400 gives the result 5904. Step 10: Now the quotient is 31.4. Step 11: Continue 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 √990 is approximately 31.46.

The approximation method is another method for finding the 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 990 using the approximation method. Step 1: Find the closest perfect square to √990. The smallest perfect square less than 990 is 961, and the largest perfect square close to 990 is 1024. √990 falls somewhere between 31 and 32. Step 2: Apply the formula: (Given number - smallest perfect square) / (Greater perfect square - smallest perfect square). Using the formula (990 - 961) / (1024 - 961) ≈ 0.4643. Add the initial integer value to the decimal value obtained: 31 + 0.4643 = 31.4643. Therefore, the square root of 990 is approximately 31.4643.

Square root: A square root is the inverse of squaring a number. For example, 4² = 16, and the inverse operation is the square root, which 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, the principal square root is always the positive square root due to its frequent use in real-world applications. Prime factorization: Breaking down a number into its prime factors. For example, the prime factorization of 990 is 2 × 3² × 5 × 11. Long division method: A method used to find square roots of non-perfect squares by dividing the number into pairs and iteratively finding the quotient.