Perform the operations and simplify: 3 sqrt 12- 5 sqrt 27+ 2sqrt 75
3 sqrt 12 - 5 sqrt 27 + 2sqrt 75
First, simplify the square roots:
3 sqrt 12 = 3 * 2√3 = 6√3
5 sqrt 27 = 5 * 3√3 = 15√3
2 sqrt 75 = 2 * 5√3 = 10√3
Combine like terms:
6√3 - 15√3 + 10√3
= (6 - 15 + 10)√3
= 1√3
So, the simplified form is:
1√3 or simply √3