How do you simplify the square root of 28 times the square root of 14?

1 Answer
Mar 24, 2018

Answer:

#14sqrt(2)#

Explanation:

You can rewrite each radicand as a product of its prime factors:
#sqrt(28) * sqrt(14) = sqrt(2*2*7) * sqrt(2*7)#

You can then separate each factor into individual radicands:
#sqrt(2*2*7) * sqrt(2*7) = sqrt(2) * sqrt(2) * sqrt(2) * sqrt(7) * sqrt(7)#

Next multiply the square roots that have a matching pair:
#sqrt(2) * sqrt(2) * sqrt(2) * sqrt(7) * sqrt(7) = 2 * sqrt(2) * 7#

Finally, simplify:
#2 * sqrt(2) * 7 = 14sqrt(2)#