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Find a degree 
Magazine Problem 1
Find the degree and a basis for the given field extension. Be prepared to justify your answers. $$ Q(\sqrt{2}) \text { over } Q $$
Problem 2
Find the degree and a basis for the given field extension. Be prepared to justify your answers. $$ Q(\sqrt{2}, \sqrt{3}) \text { over } Q $$
Problem 3
Find the degree and a basis for the given field extension. Be prepared to justify your answers. $$ Q(\sqrt{2}, \sqrt{3}, \sqrt{18}) \text { over } Q $$
Problem 4
Find the degree and a basis for the given field extension. Be prepared to justify your answers. $$ Q(\sqrt[3]{2}, \sqrt{3}) \text { over } Q $$
Problem 5
Find the degree and a basis for the given field extension. Be prepared to justify your answers. $$ Q(\sqrt{2}, \sqrt[3]{2}) \text { over } Q $$
Problem 6
Find the degree and a basis for the given field extension. Be prepared to justify your answers. $$ \mathrm{Q}(\sqrt{2}+\sqrt{3}) \text { over } \mathrm{Q} $$
Problem 7
Find the degree and a basis for the given field extension. Be prepared to justify your answers. $$ Q(\sqrt{2} \sqrt{3}) \text { over } Q $$
Problem 8
Find the degree and a basis for the given field extension. Be prepared to justify your answers. $$ Q(\sqrt{2}, \sqrt{5}) \text { over } Q $$
Problem 9
Find the degree and a basis for the given field extension. Be prepared to justify your answers. $$ Q(\sqrt[3]{2}, \sqrt[3]{6}, \sqrt[3]{24}) \text { over } \mathrm{Q} $$
Problem 10
Find the degree and a basis for the given field extension. Be prepared to justify your answers. $$ Q(\sqrt{2}, \sqrt{6}) \text { over } \mathrm{Q}(\sqrt{3}) $$
