+0  
 
-1
101
2
avatar+1317 

Help me please

 

Radicals: find the principal roots by factoring

 

1296

 

Roots:

ManuelBautista2019  Feb 1, 2018
 #1
avatar+86889 
+1

OK, Manuel

 

1296  is even, so it's divisible by 2

 

648  *  2             factor 648 

 

324 * 2 *  2        factor 324 

 

162 * 2  * 2 * 2   factor162 

 

81 * 2 * 2 * 2 *2       factor 81

 

9 * 9  * 2 * 2 * 2 * 2    factor both 9's

 

3 * 3 * 3 * 3 * 2 * 2 * 2 * 2  =

 

34 *  24           [  3 and 2 are both prime.....no further integer factorization is possible ]

 

Now  if we wanted  √1296, we would have  √[ 34 * 24]  = 

 

√3^2  *  √3^2   *   √ 2^2  *    √2^2  =

 

√9 * √9 * √4 * √4  =

 

3 * 3 * * 2   *  2  =

 

36

 

Check for yourself that 36^2  =  1296

 

 

cool cool cool

CPhill  Feb 1, 2018
 #2
avatar+1317 
-1

Thank You Cphill

ManuelBautista2019  Feb 1, 2018

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