How do you simplify #2sqrt33 - sqrt30#?

1 Answer
Apr 9, 2018

Answer:

#2sqrt3(sqrt(11) - sqrt(10))#

Explanation:

The key is to factor the numbers under the square roots and try to find a factor that is a perfect square.

For #33#, the factors are #1, 3, 11, 33#. Since none of these are perfect squares, we cannot simplify it.

For #30#, the factors are #1, 3, 5, 6, 10, 30#. Since none of these are perfect squares, we cannot simplify it.

Hence, #2sqrt(33) - sqrt(30)# is already pretty simplified.

There is one thing that you might do to "simplify", but I don't see the benefit.

You could identify that #3# is a common factor of both #30# and #33#. This allows you to factor out a #sqrt3#. You would get:

#2sqrt3(sqrt(11) - sqrt(10))#