Help. ​

³√750 + ³√2058  +  ³√48

The trick here, NSS...is to simplify the radicands as much as we can...let's factor these, first

750  =  250 * 3   =   25 * 10 * 3   =  5^2 * 5 * 2 * 3  =  5^3 * 6

2058  =   1029 * 2   =  343 * 3 * 2  =  7^3 * 6

48  =  8 * 6  =  2^3 * 6

So  we have

³√ [ 5^3 * 6 ] + ³√ [ 7^3 * 6 ]  + ³√ [ 2^3 * 6 ]  =

5³√6  + 7³√6  + 2³√6

Now just add the coefficients in front of each radical and let the radical go along for the ride..so we have

[ 5 + 7 + 2 ] ³√6  =

14³√6

4.

\(\quad\,(7-\sqrt7)(-6+\sqrt7) \\~\\ =\,(7)(-6)+(7)(\sqrt7)+(-\sqrt7)(-6)+(-\sqrt7)(\sqrt7) \\~\\ =\,-42+7\sqrt7+6\sqrt7-7 \\~\\ =\,-49+13\sqrt7\)