Name each of the following compounds:

a. CrO3 c. Al2O3 e. CaBr2
b. Cr2O3 d. NaH f. ZnCl2

If possible could you briefly explain why as well please.

https://en.wikipedia.org/wiki/Chromium%28III%29_oxide

etc, etc, etc ......

Without Google! Whats the theoretical way to solve them?

Name the metal first followed by the non-metal "stem" plus "ide".

For example
chromium oxide in a and zinc chloride in b.

To name each of the given compounds, we can follow some simple rules based on the periodic table and nomenclature conventions:

a. CrO3: In this compound, the first element is chromium (Cr) and the second element is oxygen (O). To name this compound, we use the following convention for nonmetal oxides: "element name + -ic + acid" when the oxidation number of the element is higher than the standard, which is the case here. Therefore, the name of CrO3 is chromium(VI) oxide.

b. Cr2O3: Similar to the previous compound, the first element is chromium (Cr), and the second element is oxygen (O). However, in this case, the oxidation number of chromium is different. Chromium can form both Cr(III) and Cr(VI) compounds, and in this case, it is Cr(III). For compounds where the oxidation number is lower than the standard, we use the following convention for nonmetal oxides: "element name + -ous + acid." Thus, the name of Cr2O3 is chromium(III) oxide.

c. Al2O3: In this compound, the first element is aluminum (Al), and the second element is oxygen (O). The name for this compound follows a different convention, where we use the name of the metal with a Roman numeral indicating its charge, followed by the name of the nonmetal with the suffix -ide. Thus, the name of Al2O3 is aluminum(III) oxide.

d. NaH: In this compound, the first element is sodium (Na), and the second element is hydrogen (H). Compounds that contain hydrogen often follow the convention of naming them as hydrides. Therefore, the name of NaH is sodium hydride.

e. CaBr2: In this compound, the first element is calcium (Ca), and the second element is bromine (Br). Following the naming convention for metals and nonmetals, this compound is named calcium bromide.

f. ZnCl2: In this compound, the first element is zinc (Zn), and the second element is chlorine (Cl). Similarly, we use the name of the metal with a Roman numeral indicating its charge, followed by the name of the nonmetal with the suffix -ide. Hence, the name of ZnCl2 is zinc(II) chloride.