How do you simplify #6sqrt18 + 3sqrt50#?

1 Answer
Joel Kindiak
Jun 6, 2016

#33sqrt(2)#

Explanation:

Consider #18# and #50# as products of primes:

#18 = 2 times 9 = 2 times 3^2# and #50 = 2 times 25 = 2 times 5^2#

This means that

#sqrt(18) = sqrt(2 times 3^2) = sqrt(2)sqrt(3^2) = 3sqrt(2)#

and similarly, #sqrt(50) = 5sqrt(2)#.

Thus, #6sqrt(18) + 3sqrt(50)# can be simplified as such:
#6sqrt(18) + 3sqrt(50)# = #6(3sqrt(2)) + 3(5sqrt(2)) = 18sqrt(2) + 15sqrt(2) = 33sqrt(2)#

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