Question

Solve the expression: 7√10 - √6 + 2√10. Show all your work for full credit.

Answer 1

To solve the expression 7√10 - √6 + 2√10, first simplify the square roots, then combine like terms.

Step-by-step explanation:

To solve the expression 7√10 - √6 + 2√10, we need to combine like terms. First, we can simplify the square roots. Since 10 can be expressed as 2 × 5 and 6 can be expressed as 2 × 3, we have:

7√10 - √6 + 2√10 = 7√(2 × 5) - √(2 × 3) + 2√(2 × 5)

Next, we can combine the square roots with the same radicand:

7√(2 × 5) + 2√(2 × 5) - √(2 × 3)

This simplifies to:

9√(2 × 5) - √(2 × 3)

Lastly, we can perform the multiplication:

9√10 - √6