Question

Write square root of, minus, 40, end square root
−40
​
in simplest radical form.

Answer 1

The expression you're looking at is \(\sqrt{-40}\).

To simplify this, we can note that the square root of a negative number involves the imaginary unit \(i\), where \(i = \sqrt{-1}\).

First, we can rewrite \(-40\) as:

\[
\sqrt{-40} = \sqrt{-1 \times 40} = \sqrt{-1} \times \sqrt{40}
\]

This gives us:

\[
\sqrt{-40} = i \sqrt{40}
\]

Next, we simplify \(\sqrt{40}\). We can factor \(40\) into its prime factors:

\[
40 = 4 \times 10 = 4 \times (2 \times 5)
\]

Now, since \(4\) is a perfect square, we have:

\[
\sqrt{40} = \sqrt{4 \times 10} = \sqrt{4} \times \sqrt{10} = 2\sqrt{10}
\]

Putting it all together, we get:

\[
\sqrt{-40} = i \cdot 2\sqrt{10} = 2i\sqrt{10}
\]

Thus, the simplest radical form of \(\sqrt{-40}\) is:

\[
\boxed{2i\sqrt{10}}
\]