Question

Write square root of, minus, 128, end square root
−128
​
in simplest radical form.

Answer 1

To express \(-\sqrt{128}\) in simplest radical form, we first consider the square root of 128, which can be simplified as follows:

1. Factor 128 into its prime factors:
\[
128 = 2^7
\]

2. Use the property of square roots to simplify:
\[
\sqrt{128} = \sqrt{2^7} = \sqrt{2^6 \cdot 2} = \sqrt{(2^3)^2 \cdot 2} = 2^3 \sqrt{2} = 8\sqrt{2}
\]

3. Now, we can incorporate the negative sign:
\[
-\sqrt{128} = -8\sqrt{2}
\]

Thus, the final answer in simplest radical form is:
\[
-\sqrt{128} = -8\sqrt{2}
\]