Question

1. $-5sqrt{256}$
2. $-sqrt{180}$
3. $4sqrt{50}$
4. $-6sqrt{128}$
5. $-6sqrt{108}$
6. $3sqrt{180}$
7. $-3sqrt{288}$
8. $-4sqrt{216}$
9. $8sqrt{150}$
10. $6sqrt{216}$
11. $-3sqrt{100}$

Explanation:

Step1: Simplify $\sqrt{256}$

$\sqrt{256}=16$, so $-5\sqrt{256}=-5\times16=-80$

Step2: Simplify $\sqrt{180}$

$\sqrt{180}=\sqrt{36\times5}=6\sqrt{5}$, so $-\sqrt{180}=-6\sqrt{5}$

Step3: Simplify $\sqrt{50}$

$\sqrt{50}=\sqrt{25\times2}=5\sqrt{2}$, so $4\sqrt{50}=4\times5\sqrt{2}=20\sqrt{2}$

Step4: Simplify $\sqrt{128}$

$\sqrt{128}=\sqrt{64\times2}=8\sqrt{2}$, so $-6\sqrt{128}=-6\times8\sqrt{2}=-48\sqrt{2}$

Step5: Simplify $\sqrt{108}$

$\sqrt{108}=\sqrt{36\times3}=6\sqrt{3}$, so $-6\sqrt{108}=-6\times6\sqrt{3}=-36\sqrt{3}$

Step6: Simplify $\sqrt{180}$

$\sqrt{180}=6\sqrt{5}$, so $3\sqrt{180}=3\times6\sqrt{5}=18\sqrt{5}$

Step7: Simplify $\sqrt{288}$

$\sqrt{288}=\sqrt{144\times2}=12\sqrt{2}$, so $-3\sqrt{288}=-3\times12\sqrt{2}=-36\sqrt{2}$

Step8: Simplify $\sqrt{216}$

$\sqrt{216}=\sqrt{36\times6}=6\sqrt{6}$, so $-4\sqrt{216}=-4\times6\sqrt{6}=-24\sqrt{6}$

Step9: Simplify $\sqrt{150}$

$\sqrt{150}=\sqrt{25\times6}=5\sqrt{6}$, so $8\sqrt{150}=8\times5\sqrt{6}=40\sqrt{6}$

Step10: Simplify $\sqrt{216}$

$\sqrt{216}=6\sqrt{6}$, so $6\sqrt{216}=6\times6\sqrt{6}=36\sqrt{6}$

Step11: Simplify $\sqrt{100}$

$\sqrt{100}=10$, so $-3\sqrt{100}=-3\times10=-30$

Answer:

1. $-80$
2. $-6\sqrt{5}$
3. $20\sqrt{2}$
4. $-48\sqrt{2}$
5. $-36\sqrt{3}$
6. $18\sqrt{5}$
7. $-36\sqrt{2}$
8. $-24\sqrt{6}$
9. $40\sqrt{6}$
10. $36\sqrt{6}$
11. $-30$