Questions: Consider the expression 2 sqrt(3) + 5 sqrt(2) + 5 sqrt(3) - 5 sqrt(2) Complete the statement. The expression 2 sqrt(3) + 5 sqrt(2) + 5 sqrt(3) - 5 sqrt(2) is equivalent to

Solution Steps

To simplify the expression, we need to combine like terms. The terms involving \(\sqrt{3}\) can be combined together, and the terms involving \(\sqrt{2}\) can be combined together. This will give us a simplified expression.

The given expression is \(2\sqrt{3} + 5\sqrt{2} + 5\sqrt{3} - 5\sqrt{2}\). We start by identifying like terms. The terms involving \(\sqrt{3}\) are \(2\sqrt{3}\) and \(5\sqrt{3}\), and the terms involving \(\sqrt{2}\) are \(5\sqrt{2}\) and \(-5\sqrt{2}\).

Combine the like terms:

• For \(\sqrt{3}\): \(2\sqrt{3} + 5\sqrt{3} = 7\sqrt{3}\)
• For \(\sqrt{2}\): \(5\sqrt{2} - 5\sqrt{2} = 0\)

After combining the like terms, the expression simplifies to \(7\sqrt{3} + 0\), which is simply \(7\sqrt{3}\).

Final Answer