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