Question

How do you simplify `sqrt(128)`?

Answer 1

`sqrt128=8sqrt2`

Explanation:

`sqrt128=sqrt(64*2)=sqrt64sqrt2=8sqrt2`

Answer 2

`sqrt(128) = 8*sqrt(2)`

Explanation:

The process here is to simplify radicals. Using a tree diagram, you can break down 128 into it's constituent prime number factors.

                                           128
                                           /    \
                                          2     64
                                                 /   \
                                                2   32
                                                     /   \
                                                    2   16
                                                         /   \
                                                        2    8
                                                             /   \
                                                            2   4
                                                                /   \
                                                               2   2

Counting the prime factors, the number 2 shows up seven times, so

`128 = 2^7`, which gives us `sqrt(128) = sqrt(2^7) = sqrt(2^6*2) = 2^3 * sqrt(2) = 8*sqrt(2)`