Question

find the square root of 128 in radicals

Answer 1

To find the square root of 128 in radicals, we can first factor 128 into its prime factors.

The prime factorization of 128 is:
\[
128 = 2^7
\]

Now we can express the square root of 128 using these prime factors:
\[
\sqrt{128} = \sqrt{2^7}
\]

We can simplify this by taking out pairs of factors:
\[
\sqrt{2^7} = \sqrt{(2^6) \cdot (2^1)} = \sqrt{2^6} \cdot \sqrt{2^1} = 2^3 \cdot \sqrt{2} = 8\sqrt{2}
\]

Thus, the square root of 128 in radicals is:
\[
\sqrt{128} = 8\sqrt{2}
\]