Combine the coefficients of the like surds: 2 + 4 - 1 = 5. Therefore, the expression simplifies to 5 sqrt(3).

Simplify the surds first. sqrt(45) = sqrt(9 * 5) = 3 sqrt(5). sqrt(20) = sqrt(4 * 5) = 2 sqrt(5). Subtracting them yields 3 sqrt(5) - 2 sqrt(5) = sqrt(5).

First, simplify both surds. sqrt(50) = 5 sqrt(2) and sqrt(18) = 3 sqrt(2). Now add the like surds: 5 sqrt(2) + 3 sqrt(2) = 8 sqrt(2).

These are like surds, so you just subtract the coefficients. 5 - 2 = 3, so the result is 3 sqrt(5).

Simplify each surd first. sqrt(27) = 3 sqrt(3) and sqrt(12) = 2 sqrt(3). Subtract the two expressions: 3 sqrt(3) - 2 sqrt(3) = 1 sqrt(3) or simply sqrt(3).

First, simplify sqrt(8) to 2 sqrt(2). Substitute this back into the expression: 2 sqrt(2) + sqrt(2). Adding these like terms gives 3 sqrt(2).

When adding like surds, treat them as variables (e.g., x + x = 2x). Therefore, 1 sqrt(2) + 1 sqrt(2) = 2 sqrt(2).

Identify 9 as the largest perfect square factor. Rewrite sqrt(27) as sqrt(9 * 3). The square root of 9 is 3, resulting in 3 sqrt(3).

The highest perfect square factor of 80 is 16. Break the surd into sqrt(16 * 5). Taking the square root of 16 yields 4, leaving 4 sqrt(5).

The largest perfect square factor of 108 is 36. Rewrite as sqrt(36 * 3). The square root of 36 is 6, so the result is 6 sqrt(3).