Sissy Devane said:
Simply by factoring. Asusme all expressions under radicals represent nonnegative number.
?(81 • t^8 )
This is what I have done
?(9 • t^4 ) ?(9 • t^4 )
I think I am on the right path, but I am stuck
If you are trying to simplify a cube root, then you need to look for perfect cubes under the radical sign. Here's how I would approach it:
cuberoot( 81*t[sup:2juc08zn]8[/sup:2juc08zn])
cuberoot(3[sup:2juc08zn]4[/sup:2juc08zn]*t[sup:2juc08zn]8[/sup:2juc08zn])
Now...we can write 3[sup:2juc08zn]4[/sup:2juc08zn] as 3[sup:2juc08zn]3[/sup:2juc08zn]*3, and we can write t[sup:2juc08zn]8[/sup:2juc08zn] as t[sup:2juc08zn]6[/sup:2juc08zn]*t[sup:2juc08zn]2[/sup:2juc08zn]
And we have
cuberoot(3[sup:2juc08zn]3[/sup:2juc08zn] * 3 * t[sup:2juc08zn]6[/sup:2juc08zn] * t[sup:2juc08zn]2[/sup:2juc08zn])
Do some regrouping under the radical sign:
cuberoot( (3[sup:2juc08zn]3[/sup:2juc08zn]*t[sup:2juc08zn]6[/sup:2juc08zn])* 3 * t[sup:2juc08zn]2[/sup:2juc08zn])
or,
cuberoot( 3[sup:2juc08zn]3[/sup:2juc08zn]*t[sup:2juc08zn]6[/sup:2juc08zn] ) * cuberoot( 3 * t[sup:2juc08zn]2[/sup:2juc08zn])
Now, you can take the cube root of the first expression:
3 t[sup:2juc08zn]2[/sup:2juc08zn] * cuberoot(3 t[sup:2juc08zn]2[/sup:2juc08zn])
