Find the square root of 128.(1 point)
Responses
24–√
2 start root 4 end root
82–√
8 start root 2 end root
64 −−−√ x 2–√
start root 64 end root x start root 2 end root
42–√
4 start root 2 end root
None of the given responses are the correct square root of 128. The correct answer is 8√2.
To find the square root of 128, follow these steps:
Step 1: Start with the number 128
Step 2: Break down 128 into its prime factors: 2 * 2 * 2 * 2 * 2 * 2 * 2
Step 3: Group the prime factors into pairs: (2 * 2) * (2 * 2) * (2 * 2)
Step 4: Take one factor from each pair and multiply them together:
2 * 2 * 2 = 8
Step 5: The result, 8, is the square root of 128.
So, the square root of 128 is 8, which can be written as √128 = 8.
To find the square root of 128, you can either use a calculator or simplify it manually. Here's how you can simplify it manually:
Step 1: Break down 128 into its prime factors: 128 = 2 * 2 * 2 * 2 * 2 * 2 * 2 = 2^7.
Step 2: Group the prime factors into pairs: (2 * 2) * (2 * 2) * (2 * 2) * 2 = 4 * 4 * 4 * 2.
Step 3: Take the square root of each pair: √(4 * 4) * √(4 * 4) * √(4 * 4) * √2 = 4 * 4 * 4 * √2.
Step 4: Simplify the expression: 4 * 4 * 4 = 64. Therefore, √128 = 64√2.
So, the correct answer is 64√2.