Here we have a radical that could be simplified further. I will show you how it's done with these steps: [tex] \sqrt128 [/tex] From here, you need to find a factor of 128 that is a perfect square, like 4: [tex]\sqrt(4 * 32)[/tex] [tex]= \sqrt4 * \sqrt32[/tex] [tex]= 2 * \sqrt32[/tex] [tex]= 2\sqrt32[/tex] But we're not done here since [tex]\sqrt32[/tex] can be simplified further. We know that 16 is a factor of 32 that is a perfect square. [tex]2\sqrt32[/tex] [tex]= 2\sqrt(16*2)[/tex] [tex]= 2*\sqrt16 * \sqrt2[/tex] [tex]= 2 * 4 * \sqrt2[/tex] [tex]= 8 * \sqrt2[/tex] [tex]= 8\sqrt2[/tex]
