what is the square root of 288 ?
http://www.google.com/#q=square+root+288
To find the square root of 288, we can use the following steps:
1. Start by finding the prime factorization of 288:
- 288 = 2 * 2 * 2 * 2 * 2 * 3 * 3 = 2^5 * 3^2
2. Group the prime factors in pairs, taking one factor from each pair:
- 288 = (2^2 * 3) * (2^2 * 3) * 2 = (2^2 * 3)^2 * 2
3. Take the square root of both sides of the equation:
- √288 = √[(2^2 * 3)^2 * 2] = (2^2 * 3)√2
- Simplifying further, we get:
√288 = 2 * 3 * √2 = 6√2
Therefore, the square root of 288 is 6√2.
To find the square root of 288, you can use a calculator or follow these steps:
1. Start by making an estimate. Since 17 squared is 289 (which is close to 288), you could estimate the square root to be around 17.
2. Take this estimate and divide 288 by 17. The result is approximately 16.941.
3. Now, you can improve your estimate by averaging it with the previous answer. Add 17 and 16.941, then divide by 2. The result is around 16.971.
4. Repeat step 2 with the improved estimate: divide 288 by 16.971. The result is approximately 16.962.
5. Continue this process of refining the estimate and calculating until you achieve the desired level of accuracy.
Using a calculator, the square root of 288 is approximately 16.9705627485.