Question

How to solve: sqrt3 x ( sqrt2 +sqrt6 )
answerbook says: sqrt6 + 3 sqrt2

Answer 1

=Sqrt 3 x sqrt(12)
=Sqrt 24
=sqrt 6 + sqrt 18
=sqrt 6 + sqrt (9x2)
=sqrt 6 + 3sqrt2

Answer 2

\[ \sqrt{3} ( \sqrt{2} + \sqrt{6} )\]
distribute the sqr(3):
\[ \sqrt{3} \sqrt{2} + \sqrt{3} \sqrt{6} \]
use this "rule"
\[ \sqrt{a\cdot b} = \sqrt{a} \sqrt{b} \]
and vice versa
\[ \sqrt{3} ( \sqrt{2} + \sqrt{6} )\]

to write the first term as sqrt(6) and the second term as sqrt(18):
\[ \sqrt{6}+\sqrt{18} \]
notice 18 = 9*2
so we we can write sqr(18) as sqr(9) * sqr(2) (using the rule "the other way"
\[ \sqrt{6}+\sqrt{9}\sqrt{2} \]
sqr(9)= sqr(3*3) = 3, so
\[ \sqrt{6}+3\sqrt{2} \]