Combining Radical Expressions

Intermediate Algebra: One Step at a Time.  Page 250:   #16, 17.

Simplifying radicals is not nearly as hard as you think it is, especially if it is explained in living color!  Consider these two exercises from page 250.  Notice how the colors make the exercises so much easier to follow.  Can you imagine what this would look like in black and white?  Most of our television is in color--why not math? 

First, before you even start to do #16, there are cube roots, so you must get the perfect cubes in your mind:        2³=8,    3³=27,    4³=64,    5³=125. 

16.      5  −  4

Find a perfect cube that divides into 108 (that would be 27) and a perfect cube that divides into 32 (that would be 8).  108=27x4 and 32=8x4.

            5  −  4

            5  −  4

            5 •  −  4  •

            5 • 3  •  −  4 • 2  •

Now multiply the numbers 5 times 3 and the 4 times 2.

            15     −      8

Now you have like terms so you can combine the 15 and the -8, and the final answer is  7  

In # 17, you have 4th roots, so keep in mind that 2⁴=16 and 3⁴=81.

17.      7  − 3

Find a perfect 4th power that divides into 32 (that would be 16) and a perfect 4th power that divides into 162 (that would be 81).  32=16x2 and 162=81x2.

            7  − 3

            7  − 3

             7 •  − 3 •

             7 •  2 •  − 3 • 3  •

Now multiply the numbers 7 times 2 and the 3 times 3.

            14  –  9

Now you have like terms so you can combine the 14 and the -9, and the final answer is  5  

Return to main page      Return to Intermediate Algebra page