How do you find square roots?
http://mathforum.org/dr.math/faq/faq.sqrt.by.hand.html
To find square roots, you can follow these steps:
1. Start by estimating the square root: Find the two perfect square numbers that the number you want to find the square root of falls between. For example, if you want to find the square root of 15, it falls between 3^2 (9) and 4^2 (16), so the estimated square root will be somewhere between 3 and 4.
2. Divide the number you want to find the square root of by the estimated square root. For example, divide 15 by 3: 15 ÷ 3 = 5.
3. Average the estimated square root and the result from step 2: (3 + 5) ÷ 2 = 4.
4. Repeat steps 2 and 3 with the new average as the next estimate. Divide 15 by 4: 15 ÷ 4 = 3.75.
5. Keep repeating steps 2 and 3 until the estimated square root is as precise as desired. In this case, we can round the result to two decimal places since we want an approximation. The final result is approximately 3.87.
If you want a more precise answer, you can continue the process for as long as you need, using more decimal places in each step.
For a visual demonstration and more detailed explanations, you can refer to the link provided: http://mathforum.org/dr.math/faq/faq.sqrt.by.hand.html