How do you simplify (3) [square root of (3/7)] -(5) (square root of 84)?

1 Answer
Oct 8, 2015

Answer:

#-9sqrt(21)#

Explanation:

Start by writing down your starting expression

#3sqrt(3/7) - 5sqrt(84) = 3 * sqrt(3)/sqrt(7) - 5sqrt(84)#

Thee first thing to do here is rationalize the denominator of the first term by multiplying by #1 = sqrt(7)/sqrt(7)#

This will get you

#3 * sqrt(3)/sqrt(7) * sqrt(7)/sqrt(7) = 3 * sqrt(21)/(sqrt(7) * sqrt(7)) = 3/7 * sqrt(21)#

Now focus on the second radical term. Notice that you can write #84# as

#84 = 2 * 42 = 2 * 2 * 21 = 2^2 * 21#

The expression will thus be

#3/7 * sqrt(21) - 5 * sqrt(2^2 * 21)#

#3/7 * sqrt(21) - 5 * 2sqrt(21)#

This will be equal to

#sqrt(21) * (3/7 - 10) = sqrt(21) * ((3-70)/7) = sqrt(21) * ((-63))/7#

Finally, this expression can be simplified to

#-((63))/7 sqrt(21) = color(green)(-9sqrt(21))#