Find the square root of 128.
1. 8√2
2. 2√4
3. √64 x √2
4. 4√2
The correct answer is 4√2
To find the square root of 128, we can factorize it into its prime factors: 128 = 2^7.
Next, we group the prime factors in pairs: 128 = 2 * 2 * 2 * 2 * 2 * 2 * 2.
Since there are seven 2's, we can take out two 2's from the square root: 2 * 2 = 4.
This leaves us with 2 * 2 * 2 * 2 * 2 = 32 inside the square root sign.
Therefore, the square root of 128 is 4√32.
None of the given options match this answer, so none of the provided choices are the correct answer.
To find the square root of 128, we need to identify the option that represents its simplified square root.
Let's go through each option and simplify them:
1. 8√2: This option cannot be simplified further because 8 is not a perfect square.
2. 2√4: The square root expression inside the square root sign (√4) simplifies to 2. Multiplying it by 2 gives us 4. However, this does not match the square root of 128.
3. √64 x √2: The square root of 64 is 8. Multiplying it by the square root of 2 (√2) gives us 8√2.
4. 4√2: This option cannot be simplified further because 4 is not a perfect square.
Comparing the simplified expressions from options 1 and 3, we can conclude that the correct answer is:
3. √64 x √2 = 8√2
So, the square root of 128 is 8√2.