Final answer:
To simplify the expression √20 + √45 - √5, factor each number, find perfect squares, and simplify to get 2√5 + 3√5 - √5, which simplifies further to 4√5.
Step-by-step explanation:
The student is asking how to simplify the expression √20 + √45 - √5. To simplify square root expressions, we factor each number under the square root to find perfect squares and then simplify each term separately. The number 20 can be factored into 4x5, and since 4 is a perfect square, √20 simplifies to 2√5. The number 45 can be factored into 9x5, and since 9 is a perfect square, √45 simplifies to 3√5. The simplified expression becomes 2√5 + 3√5 - √5, which can be combined because they are like terms. The sum of the coefficients 2 + 3 - 1 is 4, so the final answer is 4√5.
The simplest form of the expression √20 + √45 - s√5 can be found by simplifying each square root term separately and then combining the like terms:
√20 = √(2 · 2 · 5) = 2√5
√45 = √(3 · 3 · 5) = 3√5
- s√5 cannot be simplified any further
Combining the like terms, we have 2√5 + 3√5 - s√5 = (2 + 3 - s)√5 = (5 - s)√5
Therefore, the simplest form of the expression is (5 - s)√5.