Find the square root of 96.(1 point)
Responses
The square root of 96 is approximately 9.8.
To find the square root of 96, follow these steps:
Step 1: Start by estimating the square root. In this case, the number is close to 100, so we can estimate it to be around 10.
Step 2: Divide 96 by the estimate from step 1. 96/10 = 9.6
Step 3: Take the average of the result from step 2 and the estimate from step 1. (10 + 9.6)/2 = 9.8
Step 4: Repeat steps 2 and 3 with the new estimate. 96/9.8 = 9.8
(9.8 + 9.6)/2 = 9.7
Step 5: Continue this process of dividing and averaging until you reach a desired level of accuracy or until the decimal part becomes small enough to ignore.
By repeating these steps, you can continue to refine the estimate until you reach the square root of 96.
To find the square root of 96, you can use a calculator or follow these steps:
1. Start by estimating the square root of 96. Since 96 is between 81 (9 squared) and 100 (10 squared), we can estimate that the square root of 96 is somewhere between 9 and 10.
2. To begin the long division method, divide 96 by the estimated square root. Let's start with 9: 96 ÷ 9 = 10 remainder 6.
3. Next, bring down the first digit of the remainder, which is 6. This makes the new dividend 66.
4. Double the current quotient (the estimated square root) and place a placeholder for the next digit in the quotient. In this case, our current quotient is 9, and the placeholder is x.
5. Find the largest digit, x, such that 2 * (10x) is less than or equal to 66. In this case, x can be 5 because 2 * (105) equals 210, which is greater than 66. So, we use 4 as the next digit in the quotient.
6. Add the digit 4 to the current quotient to get 94. Now, we have 946 as the new dividend.
7. Repeat the process of doubling the current quotient and finding the largest digit, x, such that 2 * (10x + digit) is less than or equal to the new dividend, 946.
8. Continue this process until you have reached your desired level of accuracy or until you have found all the decimal places you need.
Using this long division method, you will find that the square root of 96 is approximately 9.79796.
nope it wrong
I apologize for any confusion. Let's try another method to find the square root of 96.
To find the square root of 96, we can use the prime factorization method:
1. Begin by finding the prime factorization of 96: 96 = 2^5 * 3.
2. Pair up the prime factors: (2^2) * (2^1) * 2 * 3.
3. Take one factor from each pair and bring it out of the square root: 2 * (2^2) * sqrt(3).
4. Simplify the perfect square: 2 * 4 * sqrt(3) = 8 * sqrt(3).
Therefore, the square root of 96 is 8 * sqrt(3), which is approximately 13.856.
Find the square root of 96.(1 point)
Responses
24
24
46–√
4 start root 6 end root
166–√
16 start root 6 end root
64–√
6 start root 4 end root