Find the square root of 96.(1 point)
Responses
166–√
16 start root 6 end root
64–√
6 start root 4 end root
24
24
46–√
6 start root 4 end root
To find the square root of 96, we can use a method called prime factorization.
Step 1: Prime Factorization of 96
To begin, we need to break down 96 into its prime factors. Let's start dividing it by the smallest prime number, which is 2.
Dividing 96 by 2 gives us 48, and since 48 is also divisible by 2, we can divide it again to get 24. Continuing the process, we divide 24 by 2 to get 12, and then divide 12 by 2 to get 6. Now, we have reached a point where we can't divide by 2 anymore.
Next, we move on to the next prime number, which is 3.
Dividing 6 by 3 gives us 2. Since 2 is a prime number, we stop here.
So, the prime factorization of 96 is 2^5 * 3.
Step 2: Finding the Square Root
To find the square root of 96, we can simplify the prime factorization. Since we have 2^5 * 3, we remove pairs of the same prime factors from inside the square root.
Taking out 2^2 from 96, we get 2^2 * 24. This simplifies to 2^2 * (2^2 * 6). Now, we can rewrite this as 2^2 * (2^2 * 2 * 3).
Applying the property of the square root, we take out 2 * 2 from the square root and leave the remaining 2 * 2 * 2 * 3:
sqrt(96) = 2 * 2 * sqrt(2 * 2 * 2 * 3)
We can simplify it further:
sqrt(96) = 4 * sqrt(2 * 2 * 2 * 3)
= 4 * sqrt(2^3 * 3)
= 4 * (2 * sqrt(3))
= 8 * sqrt(3)
Therefore, the square root of 96 is 8 * sqrt(3).
To find the square root of 96, follow these steps:
Step 1: Start by dividing 96 by the smallest possible number, which is 1. The result is 96.
Step 2: Now, find a number that when squared is less than or equal to 96. Let's try with 2: 2 squared is 4, which is less than 96.
Step 3: Move to the next number 3 and square it. 3 squared is 9, which is also less than 96.
Step 4: Continue this process until you find a number, let's call it x, whose square is less than or equal to 96, but the next number (x+1) squared is greater than 96.
Step 5: The number you found in step 4, in this case, is 9. So the square root of 96 is between 9 and 10.
Step 6: To get a more accurate approximation, divide 96 by 9 and get the result of 10.66.
Therefore, the square root of 96 is approximately 9.79.