Question

Need Help Please Explain I'm confused

Answer 1

OK.  Quite a bit of work for 5 points, but here goes:

Picture on the left:

When square roots need to be multiplied, just go ahead and
mash everything together. 

The product of        √one thing) times (√another thing

is just                     √(one thing times the other thing) .

So  √(3x²y³)  ·  2  ·  √(72x³y⁴)  is just

                               2 · √(3x²y³ · 72x³y⁴)

                       =      2 · √(216 x⁵ y⁷)

That looks pretty complicated.  But if you break it up into things that are
perfect squares, then you can pull those out of the square root.

                             2 · √(216 x⁵ y⁷)

                       =    2  · √(6·36  ·  x⁴·x  ·  y⁶·y)

The bold things are perfect squares, so take their square roots
and write those outside of the square root sign. 

                        =    2  · √(6·36  ·  x⁴·x  ·  y⁶·y)

                        =    2 · 6 · x² · y³ · √(6 · x · y)

                        =       12 x² y³   √6xy  .
________________________________________________

Middle picture:

How do you take the 8th root of something raised to a power ?
Just divide the power by 8 . 

                                    ⁸√(p²⁰· q²⁹ · r¹¹)

                              =    ⁸√(p¹⁶·p⁴  ·  q²⁴·q⁵  ·  r⁸·r³)

                              =   p² q³ r  ⁸√p⁴ q⁵ r³ 
____________________________________________

Picture on the right:

                           -3i (6  +  2i)

                     =    (-3i)·(6)  +  (-3i)·(2i)

                     =        -18i    +      -6i²

If ' i ' = √-1 , then i² = -1 .

                               -18i    +      -6i²

                           =  -18i    +      -6(-1)

                           =    -18i    +      6 .

Make it a little bit neater.  Factor out the ' 6 ':

                                 -18i    +      6

                           =   6·(-3i + 1) .