Question

simplify.

1. $-5\sqrt{6} - 2\sqrt{6}$\t\t\t\t2) $-3\sqrt{5} + 2\sqrt{5}$

1. $-4\sqrt{3} + 3\sqrt{3}$\t\t\t\t4) $-3\sqrt{6} - 4\sqrt{6}$

1. $-4\sqrt{10} + 5\sqrt{10}$\t\t\t\t6) $-\sqrt{6} - 2\sqrt{6}$

1. $-\sqrt{7} - 5\sqrt{7}$\t\t\t\t8) $-\sqrt{10} - 5\sqrt{10}$

1. $-3\sqrt{24} - 3\sqrt{2} + 2\sqrt{2}$\t\t\t10) $-3\sqrt{45} - \sqrt{5} + 2\sqrt{2}$

\t$-6\sqrt{6} - \sqrt{2}$

Explanation:

Problem 1: $-5\sqrt{6} - 2\sqrt{6}$

Step 1: Combine like terms

Since both terms have $\sqrt{6}$, we can factor out $\sqrt{6}$: $(-5 - 2)\sqrt{6}$

Step 2: Calculate the coefficient

$-5 - 2 = -7$, so the result is $-7\sqrt{6}$

Step 1: Combine like terms

Factor out $\sqrt{5}$: $(-3 + 2)\sqrt{5}$

Step 2: Calculate the coefficient

$-3 + 2 = -1$, so the result is $-\sqrt{5}$

Step 1: Combine like terms

Factor out $\sqrt{3}$: $(-4 + 3)\sqrt{3}$

Step 2: Calculate the coefficient

$-4 + 3 = -1$, so the result is $-\sqrt{3}$

Answer:

$-7\sqrt{6}$

Problem 2: $-3\sqrt{5} + 2\sqrt{5}$