Question

Simplifying radicals! Please help me & Show WORK

Answer 1

Solving the radical
`4√(2)(-4√(15)+3√(18))` we get
`\mathbf{-16√(30)+72}`

Explanation:

We need to simplify the radical:
`4√(2)(-4√(15)+3√(18))`

Prime factors of 18 are: 2x3x3

Replacing
`√(18)` with its factors

`4√(2)(-4√(15)+3√(18))\\=4√(2)(-4√(15)+3√(2*3*3))\\=4√(2)(-4√(15)+3√(2*3^2))`

We know that
`√(3^2)=3`

`=4√(2)(-4√(15)+3*3√(2))\\=4√(2)(-4√(15)+9√(2))`

Multiplying
`4√(2)` with terms inside the bracket

`=4√(2)(-4√(15))+4√(2)( 9√(2)))\\=-16√(2)√(15)+36√(2) √(2)`

We know that
`√(2) √(2)=2`

`=-16√(2*15)+36(2)\\=-16√(30)+72`

So, solving the radical
`4√(2)(-4√(15)+3√(18))` we get
`\mathbf{-16√(30)+72}`