square root of 96
The square root of 96 is approximately 9.80
To find the square root of 96, follow these steps:
Step 1: Prime factorize the number 96.
96 = 2 * 2 * 2 * 2 * 2 * 3 = 2^5 * 3
Step 2: Group the prime factors in pairs and represent them as square roots.
√96 = √(2^5 * 3)
Step 3: Take out the pairs from under the square root.
√(2^2 * 2^2 * 2 * 3) = √(2^2) * √(2^2) * √(2) * √(3) = 2 * 2 * √2 * √3 = 4√6
So, the square root of 96 is 4√6.
To find the square root of 96, you can follow these steps:
1. Start by recognizing any perfect square factors of 96. The perfect square numbers that are less than 96 include 1, 4, 9, 16, 25, 36, 49, and 64.
2. The largest perfect square that divides evenly into 96 is 16 (since 16 x 6 = 96).
3. Write 96 as a product of the largest perfect square factor and the remaining factor: 96 = 16 x 6.
4. Now, we can simplify the expression by taking the square root of the perfect square factor and leaving the remaining factor as it is: √(96) = √(16 x 6).
5. The square root of 16 is 4 since 4 x 4 = 16.
6. The square root of 6 is an irrational number and cannot be expressed as a simple fraction or decimal. So, we leave it as is.
7. Combine the simplified square roots: √(96) = 4√6.
Therefore, the square root of 96 is 4√6.