How do you simplify #5sqrt17+17sqrt5#?

1 Answer
Sep 4, 2016

Answer:

#5sqrt(17)+17sqrt(5)# is already in simplest form.

Explanation:

The numbers #5# and #17# are unrelated primes, so it is not possible to combine their square roots to simplify this expression.

If you wished, you could express it differently as:

#5sqrt(17)+17sqrt(5) = sqrt(5)^2sqrt(17)+sqrt(17)^2sqrt(5)#

#color(white)(5sqrt(17)+17sqrt(5)) = sqrt(5)sqrt(17)(sqrt(5)+sqrt(17))#

#color(white)(5sqrt(17)+17sqrt(5)) = sqrt(85)(sqrt(5)+sqrt(17))#

but I would not call that simpler.