Find the square root of 96.
6√4
16√6
24
4√6
8√6
To find the square root of 96, we can simplify the square root expression.
First, let's separate the number 96 into its prime factors: 96 = 2^5 x 3.
Next, let's pair the prime factors in pairs: 2^5 x 3 = (2^2 x 2^2) x 3 = 4 x 4 x 3.
Now, we can simplify the expression: √96 = √(4 x 4 x 3) = 4√3.
Therefore, the square root of 96 is 4√3.
To find the square root of 96, we can use a calculator or manually find an approximation using the following steps:
Step 1: Start by finding the prime factorization of 96.
96 can be written as 2 × 2 × 2 × 2 × 2 × 3.
Step 2: Group the prime factors into pairs.
We can pair two 2's together because the square root requires pairs.
2 × 2 can be simplified as 2^2.
Step 3: Write the square roots separately.
The square root of 2^2 is 2.
Step 4: Multiply the different square roots together:
2 × 2 × √3
So, the simplified square root of 96 is 4√6.