Square Root of -99

The square root is the inverse of the square of the number. Since -99 is a negative number, its square root is not a real number. The square root of -99 is expressed in terms of the imaginary unit 'i'. In radical form, it is expressed as √-99, which can be rewritten as √99 * i. The value of √99 is approximately 9.95, so the square root of -99 is approximately 9.95i.

To find the square root of a negative number, we use the concept of imaginary numbers. The square root of -99 can be found by first finding the square root of 99 and then multiplying it by 'i'. Let us now learn the methods: Imaginary unit method

The imaginary unit method involves using 'i', where i² = -1. The square root of a negative number is found by taking the square root of its absolute value and multiplying by 'i'.

Step 1: Find the square root of 99, which is approximately 9.95.

Step 2: Multiply this value by 'i' to account for the negative sign inside the square root. Thus, the square root of -99 is approximately 9.95i.

The long division method can be used to find the square root of 99, which is a necessary step in finding √-99. Let us learn how to find the square root of 99 using the long division method, step by step:

Step 1: Group the digits of 99 as 99.

Step 2: Find a number whose square is less than or equal to 99. In this case, 9² = 81 is the closest.

Step 3: Subtract 81 from 99 to get 18.

Step 4: Bring down 00 to make it 1800.

Step 5: Double the divisor (9), which gives 18. Determine the next digit of the quotient such that 18n ≤ 1800.

Step 6: Continue the process to get the decimal value. The approximate value of √99 is 9.95.

The approximation method is another way to find the square root of 99. Here’s how to approximate the square root of 99:

Step 1: Identify the closest perfect squares. For 99, they are 81 (9²) and 100 (10²).

Step 2: 99 is closer to 100, so the square root of 99 is closer to 10 but slightly less.

Step 3: By interpolation, approximate the square root as 9.95. Thus, the square root of -99 is approximately 9.95i.

• Imaginary Number: An imaginary number is a number that can be written as a real number multiplied by the imaginary unit 'i', where i² = -1.
   
• Complex Number: A complex number consists of a real part and an imaginary part, written as a + bi.
   
• Real Number: A real number is any positive or negative number, including zero, that does not involve 'i'.
   
• Square: A square is a number multiplied by itself.
   
• Square Root: A square root of a number is a value that, when multiplied by itself, gives the original number.