First, simplify each radical term:
√27 = √(93) = 3√3√45 = √(95) = 3√5√20 = √(45) = 2√5√12 = √(43) = 2√3√80 = √(16*5) = 4√5
Now substitute these simplifications back into the expression:
(3√3 - 3√5 - 2√5) - (3√3 - 4√5)
Now distribute the negative sign through the second parenthesis:
3√3 - 3√5 - 2√5 - 3√3 + 4√5
Combine like terms:
(3√3 - 3√3) + (-3√5 - 2√5 + 4√5)0 - √5 = -√5
Therefore, the final answer is -√5.
First, simplify each radical term:
√27 = √(93) = 3√3
√45 = √(95) = 3√5
√20 = √(45) = 2√5
√12 = √(43) = 2√3
√80 = √(16*5) = 4√5
Now substitute these simplifications back into the expression:
(3√3 - 3√5 - 2√5) - (3√3 - 4√5)
Now distribute the negative sign through the second parenthesis:
3√3 - 3√5 - 2√5 - 3√3 + 4√5
Combine like terms:
(3√3 - 3√3) + (-3√5 - 2√5 + 4√5)
0 - √5 = -√5
Therefore, the final answer is -√5.