Find the square root of 128.
4sqrt(2)
2sqrt(4)
sqrt(64) * x * sqrt(2)
8sqrt(2)
The correct answer is 8sqrt(2).
To find the square root of 128, you can simplify it by factoring out the perfect squares from the number.
128 = 64 * 2
Taking the square root of each perfect square, we get:
√128 = √(64 * 2)
Applying the property of square roots, which states that the square root of a product is equal to the product of the square roots, we can rewrite this as:
= √64 * √2 * 1
Since the square root of 64 is 8, we have:
= 8√2
Therefore, the simplified form of the square root of 128 is 8√2.
To find the square root of 128, we can follow these steps:
1. Express 128 as a product of its prime factors: 128 = 2 * 2 * 2 * 2 * 2 * 2 * 2 = 2^7
2. Take out pairs of the same prime factors from under the square root sign: √(2^7) = √(2^6 * 2) = 2^3 * √2 = 8√2
Therefore, the square root of 128 is 8√2.
Among the options you provided, the correct answer is 8√2.