Question 72882
<pre>
solutions-using imaginary number units 


      solving 

A. square root of -48, 

            {{{sqrt(-48)}}}

            {{{sqrt (-1*16*3)}}}

            {{{sqrt(-1)}}} * {{{sqrt(16)}}} * {{{sqrt(3)}}}

Remember that {{{sqrt(-1)}}} = i


              4i {{{sqrt(3)}}}
 



B. square root of -9, 

           {{{sqrt(-9)}}}

           {{{sqrt(-1*9)}}}

           {{{sqrt(-1)}}} * {{{sqrt(9)}}}


                    3i



C. square root of -23, 

         {{{sqrt(-23)}}}

         {{{sqrt(-1)}}} * {{{sqrt(23)}}}


              i {{{sqrt(23)}}}




D. square root of - 5/9, 

      {{{sqrt(-5/9)}}}

        {{{sqrt(-5)}}}
       _________
        {{{sqrt(9)}}}


        {{{sqrt(-1)}}} * {{{sqrt(5)}}}
       _________________
         {{{sqrt(9)}}}


       1
      ___ i {{{sqrt(5)}}}
       3



E. square root of -17/16

{{{sqrt(-17/16)}}}

       {{{sqrt(-17)}}}
       _________
        {{{sqrt(16)}}}


       {{{sqrt(-1)}}} * {{{sqrt(17)}}}
       __________________
         {{{sqrt(16)}}}



         1
       _____ i  {{{sqrt(17)}}}
         4