Home > Algebra > Addition and Subtraction of Radicals

How do you simplify #2sqrt33 - sqrt30#?

Answer 1

Abigail Allen

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

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))#

By signing up, you agree to our Terms of Service and Privacy Policy

Answer 2

Ethan Adkins

To simplify 2√33 - √30, we need to find the largest perfect square that divides both 33 and 30. The largest perfect square that divides both numbers is 9.

So, we can rewrite 2√33 - √30 as 2√(93) - √(910).

Simplifying further, we get 2√9√3 - √9√10.

Since √9 is equal to 3, we can simplify it as 2*3√3 - 3√10.

Finally, the simplified form of 2√33 - √30 is 6√3 - 3√10.

By signing up, you agree to our Terms of Service and Privacy Policy

Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.