Simplify √(15) ( - √(3n) + 4n) please show all work!​

Question

Simplify

`√(15) ( - √(3n) + 4n)`
please show all work!​

Answer 1

Laws to be used:-

`\boxed{\sf a(b+c)=ab+bc}`

`\boxed{\sf √(p)√(q)=√(pq)}`

Solution

`\\ \rm\longmapsto √(15)(-√(3n)+4n)`

`\\ \rm\longmapsto -√(15)√(3n)+4√(15)n`

`\\ \rm\longmapsto -√(3(15)n)+4√(15)n`

`\\ \rm\longmapsto -√(3(3)(5)n)+4√(15)n`

`\\ \rm\longmapsto -3√(5)n+4√(15n)`

Or we can break 15n

`\\ \rm\longmapsto -3√(5)n+4√(3(5)n)`

`\\ \rm\longmapsto -3√(5)n+4√(3)√(5n)`

Answer 2

`\displaystyle - 3 √(5n) + 4 √(15) n`

Explanation:

we would like to simplify the following expression:

`\displaystyle √(15) ( - √(3n) + 4n)`

recall distribution property thus:

`\displaystyle - √(3n) √(15) + 4n √(15)`

remember that,

• 
  `\displaystyle √(a) √(b) = √(ab)`

so assign variables:

• 
  `a \implies 3n`
• 
  `b \implies 15`

simplify Multiplication:

`\displaystyle - √(45n) + 4 √(15) n`

rewrite 45 as 9×5:

`\displaystyle - √(9 * 5n) + 4 √(15) n`

utilize the formula:

`\displaystyle - √(9 ) √(5n) + 4 √(15) n`

simplify square:

`\displaystyle \boxed{- 3 √(5n) + 4 √(15) n}`

and we're done!