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42 votes
42 votes
Simplify

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

User Shilan
by
2.6k points

2 Answers

28 votes
28 votes

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)

User P Ackerman
by
2.5k points
29 votes
29 votes

Answer:


\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!

User Gil Zellner
by
3.0k points