Final answer:
To simplify the expression √80 - 2√45, we factor out perfect squares from under the square roots and consolidate terms, ending up with -2√5.
Step-by-step explanation:
The question requires simplifying the expression: √80 - 2√45, which involves the concept of simplifying square roots. First, we find the prime factorization of the numbers inside the square roots to identify perfect squares that can be taken out of the square root.
For √80:
√80 = √(16 × 5) = √16 × √5 = 4√5
For 2√45:
2√45 = 2√(9 × 5) = 2 × √9 × √5 = 6√5
Therefore, the simplified expression is:
4√5 - 6√5 = -2√5