Question 578585
{{{sqrt(18)-sqrt(54)-2sqrt(50)}}}
The trick to simplifying radicals is writing the number under the radical sign as a product of a perfect square and the smallest possible number.
Sometimes the prime factorization helps. Other times, I see it without thinking of prime factors. For example, I know that {{{50=2*25}}} and that 25 is a perfect square ({{{25=5^2}}}).
I am going to use {{{54=6*9}}} and {{{18=2*9}}} too.
{{{sqrt(18)-sqrt(54)-2sqrt(50)=sqrt(9*2)-sqrt(9*6)-2sqrt(25*2) =sqrt(9)*sqrt(2)-sqrt(9)*sqrt(6)-2sqrt(25)*sqrt(2)=3sqrt(2)-3sqrt(6)-2*5sqrt(2)=3sqrt(2)-10sqrt(2)-3sqrt(6)=-7sqrt(2)-3sqrt(6)}}}