How do you simplify 21sqrt2+6sqrt621√2+6√6?

1 Answer
Stefan V.
Oct 16, 2015

3sqrt(2)* ( 7 + 2sqrt(3))3√2⋅(7+2√3)

Explanation:

There's really not much you can do to simplify this expression.

You can, however, rewrite sqrt(6)√6 as

sqrt(6) = sqrt(2 * 3) = sqrt(2) * sqrt(3)√6=√2⋅3=√2⋅√3

The expression becomes

21sqrt(2) + 6 * sqrt(2) * sqrt(3)21√2+6⋅√2⋅√3

Notice that you can now use 3sqrt(2)3√2 as a common factor for the two terms to get

3 * 7 * sqrt(2) + 2 * 3 * sqrt(2) * sqrt(3) = 3sqrt(2)* ( 7 + 2sqrt(3))3⋅7⋅√2+2⋅3⋅√2⋅√3=3√2⋅(7+2√3)

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