Answer:
Solving the radical [tex]4\sqrt{2}(-4\sqrt{15}+3\sqrt{18})[/tex] we get [tex]\mathbf{-16\sqrt{30}+72}[/tex]
Step-by-step explanation:
We need to simplify the radical: [tex]4\sqrt{2}(-4\sqrt{15}+3\sqrt{18})[/tex]
Prime factors of 18 are: 2x3x3
Replacing [tex]\sqrt{18}[/tex] with its factors
[tex]4\sqrt{2}(-4\sqrt{15}+3\sqrt{18})\\=4\sqrt{2}(-4\sqrt{15}+3\sqrt{2\times3\times3})\\=4\sqrt{2}(-4\sqrt{15}+3\sqrt{2\times3^2})[/tex]
We know that [tex]\sqrt{3^2}=3[/tex]
[tex]=4\sqrt{2}(-4\sqrt{15}+3\times3\sqrt{2})\\=4\sqrt{2}(-4\sqrt{15}+9\sqrt{2})[/tex]
Multiplying [tex]4\sqrt{2}[/tex] with terms inside the bracket
[tex]=4\sqrt{2}(-4\sqrt{15})+4\sqrt{2}( 9\sqrt{2}))\\=-16\sqrt{2}\sqrt{15}+36\sqrt{2} \sqrt{2}[/tex]
We know that [tex]\sqrt{2} \sqrt{2}=2[/tex]
[tex]=-16\sqrt{2*15}+36(2)\\=-16\sqrt{30}+72[/tex]
So, solving the radical [tex]4\sqrt{2}(-4\sqrt{15}+3\sqrt{18})[/tex] we get [tex]\mathbf{-16\sqrt{30}+72}[/tex]
