Find the square root of 128.(1 point)
Responses
42–√
4 start root 2 end root
82–√
8 start root 2 end root
64 −−−√ x 2–√
start root 64 end root x start root 2 end root
24–√
4 start root 2 end root
To find the square root of 128, we can use the following steps:
1. Express 128 as a product of its prime factors: 128 = 2^7.
2. Take out pairs of similar factors from under the square root: √(2^7) = 2^3 * √2.
3. Simplify: √(2^7) = 8√2.
Therefore, the square root of 128 is 8√2.
To find the square root of 128, we can use a calculator or manually calculate it.
Using a calculator:
1. Enter the number 128.
2. Press the square root button (√).
3. The result should be approximately 11.3137.
Manually calculating:
We need to find the largest perfect square that is less than or equal to 128. In this case, it is 64.
1. Divide 128 by 64: 128 ÷ 64 = 2.
2. Take the average of the result and the divisor: (2 + 64 ÷ 2) ÷ 2 = (2 + 32) ÷ 2 = 34 ÷ 2 = 17.
3. Divide 128 by the average: 128 ÷ 17 = 7.529.
4. Take the average of the result and the divisor: (7.529 + 17) ÷ 2 = 24.2645 ÷ 2 = 12.1322.
5. Repeat Step 3 and Step 4 until the desired precision is achieved.
6. The square root of 128 is approximately 11.3137.