Question

Which term is correct when simplifying √128?

A.) 16
B.) 12
C.) 10
D.) 8√2

Answer 1

when dealing with roots, we want to factor to see if it's possible


`image`

`= 2 * 2 * 32`

`= 2 * 2 * 2 * 16`

`= 2 * 2 * 2 * 2 * 8`

`= 2 * 2 * 2 * 2 * 2 * 4`

`= 2 * 2 * 2 * 2 * 2 * 2 * 2`

now since we're dealing with square roots, we circle every pair of numbers we see in the final factoring
so..

`= (2 * 2) * (2 * 2) * (2 * 2) * 2`

now for every circled pair, we take only 1 of the 2 circled and bring it outside
anything left uncircled stays inside the root
so..

`= 2 * 2 * 2 * √(2)`

now simply multiply

`8 √(2)`