We are asked to simplify [tex]2 \sqrt{10} * 3 \sqrt{12} [/tex].
i) using the property :
[tex] \sqrt{a} * \sqrt{b} = \sqrt{ab} [/tex]
we write [tex]2 \sqrt{10} * 3 \sqrt{12}[/tex]
as [tex]2*3* \sqrt{10} *\sqrt{12}=6 \sqrt{120} [/tex]
ii) we factorize 120 to see whether there are perfect squares, to take out of the square root.
[tex]120=12*10=3*4*2*5= 2^{2} *3*2*5=2^{2}*30[/tex]
thus,
[tex]6 \sqrt{120}=6 \sqrt{2^{2}*30} =6* \sqrt{ 2^{2} } * \sqrt{30} =6*2* \sqrt{30}=12 \sqrt{30}[/tex]
Answer: C) [tex]12 \sqrt{30} [/tex]
