Question

Write the term in simplest form and then simplify the expression

(Surds)


`3 √(24) - 7 √(54) - √(96) + 4 √(20)`

Answer 1

Answer:
`\bold{-19√(6)+8√(5)}`

Explanation:

`.\quad 3√(24)-7√(54)-√(96)+4√(20)\\\\=3\sqrt{\underline{2\cdot 2}\cdot2 \cdot3}-7\sqrt{2\cdot 3\cdot\underline{3\cdot 3}}-\sqrt{\underline{2\cdot 2}\cdot \underline{2\cdot 2}\cdot 2\cdot 3}+4\sqrt{\underline{2\cdot 2}\cdot 5}\\\\=2\cdot 3√(2 \cdot3)-3\cdot 7√(2\cdot 3)-2\cdot 2√(2\cdot 3)+2\cdot 4√(5)\\\\=6√(6)-21√(6)-4√(6)+8√(5)\\\\=-19√(6)+8√(5)`