How do you simplify #6sqrt343 - 2 sqrt7#?

1 Answer
Mar 16, 2018

Answer:

See a solution process below:

Explanation:

First, rewrite the radical on the left as:

#6sqrt(49 * 7) - 2sqrt(7)#

Next, use this rule for radicals to simplify the term on the left:

#sqrt(color(red)(a) * color(blue)(b)) = sqrt(color(red)(a)) * sqrt(color(blue)(b))#

#6sqrt(color(red)(49) * color(blue)(7)) - 2sqrt(7) =>#

#6sqrt(color(red)(49))sqrt(color(blue)(7)) - 2sqrt(7) =>#

#(6 * 7sqrt(color(blue)(7))) - 2sqrt(7) =>#

#42sqrt(color(blue)(7)) - 2sqrt(7)#

Now, factor out the common term to complete the simplification:

#(42 - 2)sqrt(7) =>#

#40sqrt(7)#