Radical Rules

Radical Rules

√36 = 6

Try to find out if the radicand has any perfect squares within it. (like 4 and 9).. when multiplied together equal, for example, 36.

√(4)(9)
√4 * √9

 Since 4 and 9 are perfect squares, you can easily find out what number times itself equals them. ( 2*2= 4, 3*3= 9).

2*3 = 6

So, √36 = 6.   Or √4/9 = √4 / √9 = 2/3

Mixed Radical

Example:
√80 
Find the factors of 80. Factor Tree:                      

After, you are left with 2* 2* 2* 2 * 5. 

= √(2x2)(2x2)x5
Two groups of 2's. So 4^2 * 5.
= √4^2 * √5= 4√5Simplify:√63= √9 * 7 = √9 * √7 ^^^ Perfect square! (9)= 3√7                  √63 is between perfect squares √49 and √64. The estimate will be closer around 7.9, since is closer to √64. 
√49 = 7
√63 = 7.9 (guess) ... 7.937253933193772 (actually answer)√64 = 8
Radicals are the opposite of powers.

Mixed Radicals...again.

a√x .. The 'a' value has been simplified or removed from the radical.

Entire         <--->                Mixed√12                                       2√3√32                                       4√2 ....
ex: √32 = √16 * 2 = √16 * √ 2 = 4√2 .. (4x4=16)
or: √32
      = √8 * √4
      = √2 * √4 * 2 = 4√2

Simplify:

√500                      √125                      √96                      √200                       √90                 √112
√100 * √5             √25 * √5               √16 * √6                √100 * √2                  √9 * √10         √16 * √7
=10√5                   = 5√5                  = 4√6                   = 10√2                      = 3√10            = 4√7MIxed Radicals to Entire Radicals
4√3                                           6√5                          7³√5
√4^2 * √3                                √6^2 * √5                    ³√7³^³ * √5 √16 * √3                                √36 * √5                     ³√7³ * 5
√16 * 3                                  √36 * 5                     = ³√1715
=√48                                    = √180

Or try it backwards.

√48√16 * 3√16 * √3√4^2 * √34√3


Write the following from smallest to largest
2√2 , 3√3 , 4√7 , √42 , √12

For the first 3 radicals, you multiply the radicand by itself and then the outisde number.
so, 2x2= 4 x 2 = 8. (perfect square in there.. )
3x3=9x3= 27  and so on.

Here is a video that may be helpful!