To solve the given problem, we need to find the square root of the number 11001 and express that square root in binary. Let's go through the steps in detail:
1. Given Number:
The given number is 11001 in decimal.
2. Calculate the Square Root:
We need to find the square root of 11001. The square root of 11001 is approximately 104.88565202161828.
3. Convert the Square Root to Binary:
To convert the decimal number 104.88565202161828 to binary, we first consider the integer part and then the fractional part:
- Integer Part: The integer part of 104.88565202161828 is 104. To convert 104 to binary:
- 104 divided by 2 is 52 with a quotient remainder of 0 (least significant bit).
- 52 divided by 2 is 26 with a quotient remainder of 0.
- 26 divided by 2 is 13 with a quotient remainder of 0.
- 13 divided by 2 is 6 with a quotient remainder of 1.
- 6 divided by 2 is 3 with a quotient remainder of 0.
- 3 divided by 2 is 1 with a quotient remainder of 1.
- 1 divided by 2 is 0 with a quotient remainder of 1 (most significant bit).
Reading the remainders from bottom to top, the binary representation of 104 is `1101000`.
Thus, the square root of 11001 in binary is `1101000`.
Final Answer:
- The square root of 11001 is approximately 104.88565202161828.
- The binary representation of the integral part of this square root is `1101000`.
