Find the cubic root 32.

The cubic root of 32 is denoted as \(\sqrt[3]{32}\).

To find the cubic root, we can express 32 as a power of 2:
\[
32 = 2^5
\]
Now, we can use the property of roots that states \(\sqrt[3]{a^b} = a^{b/3}\):
\[
\sqrt[3]{32} = \sqrt[3]{2^5} = 2^{5/3}
\]

To simplify further, we can express \(2^{5/3}\) as:
\[
2^{5/3} = 2^{1 + 2/3} = 2^1 \cdot 2^{2/3} = 2 \cdot \sqrt[3]{4}
\]

So, the cubic root of 32 can also be expressed as \(2 \cdot \sqrt[3]{4}\).

However, if you just want the numeric value:
\[
\sqrt[3]{32} \approx 3.1748
\]

So, the answer in simplified radical form can be expressed as \(2 \cdot \sqrt[3]{4}\) or approximately \(3.1748\).

Find the square of 45.

To find the square of 45, you multiply 45 by itself:

\[
45^2 = 45 \times 45 = 2025
\]

Thus, the square of 45 is \(2025\).