I need help on how to simplify radicals?

Question

These are some of my problems, I need to know how to work out.

#1 -√144a^2

#2 √128x^3

#3 √16c^2 d^2

#4 2√27x^5 y

#5 -√320y^9 z^10

Thanks for any help you can give. I'm at my wits end.

Answer 1

Don't let your wits end...

You need to look for factors of your radicand (that's the expression under the radical) that are perfect squares.  You know what a perfect square is ?  If no, please  look it up.

Here is an example:  sqrt(32) is the same as sqrt(4 * 4 * 2)

A perfect square under the radical ( in this case 4 * 4) becomes 4 outside the radical.  The simplified radical for sqrt(32) = 4sqrt(2)

I'll do one of yours...

#4  2sqrt(27x^5y) = 2sqrt(3*3*3*(x^2)*(x^2)*x*y)

I replaced 27 with 3*3*3 and x^5 with (x^2)(x^2)x

Do you see that ?

since 3*3 is a perfect square, it will become 3 outside the radical.

same for (x^2)(x^2).  that will be x^2 outside the radical

So, 2sqrt(27x^5y) = 6x^2sqrt(3xy)

Look in your book for more examples.  The symbols on the keypad are just not the greatest.

I think you may be able to do the others.  Good luck.

Answer 2

1 -√144a^2  -  12a

#2 √128x^3  -  8x√2x

#3 √16c^2 d^2  -  4cd

#4 2√27x^5 y  -  6x^2√3xy

#5 -√320y^9 z^10   -   8y^4z^5√5y