(surds) write this in the simplest form and then simplify the expression √(128) - 5 √(27) + 2 √(32) - 3 √(75)

Question

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


`√(128) - 5 √(27) + 2 √(32) - 3 √(75)`

Answer 1

Answer:
`\bold{√(2)-15√(3)}`

Explanation:

`.\quad √(128)-5√(27)+2√(32)-3√(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√(2)-3\cdot 5√(3)+2\cdot 2\cdot 2√(2)-5\cdot 3√(2)\\\\=8√(2)-15√(3)+8√(2)-15√(2)\\\\=√(2)-15√(3)`