How do you simplify #sqrt33-sqrt9#?

1 Answer

Answer:

Find what is common in the 2 expressions, then factor it out to get to
#sqrt(3) * (sqrt(11)-sqrt(3))#

Explanation:

When we look to "simplify", most times we are looking to combine the terms in a different way than the one presented.

Take this question for example - we want to find a way to combine the two square roots into one expression. To do that, we need to find what is common about them.

#sqrt(33) - sqrt(9)#

let's break down the 33 and 9 into they're respective factors

#sqrt(11 * 3) - sqrt (3 * 3)#

and I can express this in a different way

#(sqrt(11) * sqrt(3)) - (sqrt(3)*sqrt(3))#

Each expression has a #sqrt(3)#, so let's factor that out

#sqrt(3) * (sqrt(11)-sqrt(3))#

And that is the final answer (remember that #sqrt(11)# and #sqrt(3)# are different numbers, so can't simply be subtracted to get #sqrt(8)#)