Question

(surds) write this in the simplest form and then simplify the expression

Answer 1

Answer:   $\bold{\sqrt{2}-15\sqrt{3}}$

Step-by-step explanation:

$.\quad \sqrt{128}-5\sqrt{27}+2\sqrt{32}-3\sqrt{75}\\\\=\sqrt{\underline{2\cdot 2}\cdot \underline{2\cdot 2}\cdot \underline{2\cdot 2}\cdot 2}-5\sqrt{\underline{3\cdot 3}\cdot 3}+2\sqrt{\underline{2\cdot 2}\cdot \underline{2\cdot 2}\cdot 2}-3\sqrt{2\cdot \underline{5\cdot 5}}\\\\=2\cdot 2\cdot 2\sqrt{2}-3\cdot 5\sqrt{3}+2\cdot 2\cdot 2\sqrt{2}-5\cdot 3\sqrt{2}\\\\=8\sqrt{2}-15\sqrt{3}+8\sqrt{2}-15\sqrt{2}\\\\=\sqrt{2}-15\sqrt{3}$