- Radicals can be added; 3
^{4}√15 + 4^{4}√15 = 7^{4}√15

notice that the indices (plural for index) and radicands are the same

and we added the coefficients 3 and 4

Try the following example:

5^{3}√16 + 7^{3}√2 = answer

7√16 + 7√2 = answer - Radicals can be subtracted 3
^{4}√15 - 5^{4}√15 = - 2^{4}√15

Notice that the indices and radicands are the same

and we subtracted the coefficients 3 and - 5 which = -2

Try the following example:

4^{3}√16 - 7^{3}√2 = answer

4^{3}√16 - 7^{3}√2 = answer

-5^{3}√16 - (-7)^{3}√2 = answer - Radicals can be multiplied;

4^{3}√9 x^{3}√81 =

4^{3}√9 x^{3}√3(27) =

4^{3}√9 x 3^{3}√3 =

12^{3}√27 = 36

Notice that the indices are the same and hence you can multiply the 4 and 3 which equals 12. Plus you can multiply the 9 and 3 under the radical sign which equals 27.

Next you can take the cube root of 27 which is 3 and multiple it by 12 so that your final answer is 36. - Radicals can be divided if the indices are the same.
^{3}√16 /^{3}√8 =^{3}√2

^{4}√18 /^{4}√9 = answer

^{5}√12 /^{5}√6 = answer

- Radicals can be written with fractional exponents. So
^{3}√8 can be written as 8^{1/3}^{4}√A^{3}can be written as A^{3/4}

^{7}√12^{3}= answer

^{19}√6^{7}= answer

next

return

5

4 √24 x √32 = answer

7 ^{3}√9 x 6 ^{3}√81 = answer