Radicals are treated like variables. If you can do it with a variable, you can do it with a radical.

    __         __

√3 + √2        Compare:  X + Y

                                                                                        __         __

You cannot add X + Y, so you cannot add √3 + √2 

   ___           ___

√3   x  √2       Compare:  XY

                                                                        __        __           __

You can multiply X and Y, so you can muliply √3 and √2     =   √6

Simplify:

        __                                                                              __ __      __

1)  √54    Break down the square root of 54 as follows:  √9 √6 = 3√6

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2)  √24

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3)  √90

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4)  √48

        ___

5) 3√60

Add:

1)  √35 + √28

2)  √32 + 4√18

3)  10√8 + 5√2

Multiply:

        __      __

1) (√50) (√18)

           __       _

2)  (2√12)(3√8)

          __     _      __

3)  (9√45)(√6)(2√24)

1. a. Find the perimeter of a rectangle that has a length of  √12 and a width of √3.

         Express your answer in simplest radical form.

    b. Find the area of the same rectangle in simplest form.

2. The sides of a triangle have lengths √63, √175, and 2√7. Determine its perimeter in simplest radical form.