Sir, I wanted it as a sum of surds; not a product of surds.

Asked by bjayanta | 12th Jun, 2015, 01:19: PM

Expert Answer:

Another way of approaching the same problem is as follows:
2 to the power of 1 divided by 3 end exponent minus 1 equals open parentheses open parentheses 2 to the power of 1 divided by 3 end exponent minus 1 close parentheses cubed close parentheses to the power of 1 divided by 3 end exponent equals open parentheses open parentheses 2 to the power of 1 divided by 3 end exponent close parentheses cubed minus 1 cubed minus 3 cross times 2 to the power of 1 divided by 3 end exponent cross times 1 open parentheses 2 to the power of 1 divided by 3 end exponent minus 1 close parentheses close parentheses to the power of 1 divided by 3 end exponent equals open parentheses 2 minus 1 minus 3 cross times 2 to the power of 2 divided by 3 end exponent plus 3 cross times 2 to the power of 1 divided by 3 end exponent close parentheses to the power of 1 divided by 3 end exponent equals open parentheses 1 minus 3 cube root of 4 plus 3 cube root of 2 close parentheses to the power of 1 divided by 3 end exponent equals cube root of 1 minus 3 cube root of 4 plus 3 cube root of 2 end root H e n c e comma space c u b e space r o o t space o f space 2 to the power of 1 divided by 3 end exponent minus 1 equals root index 9 of 1 minus 3 cube root of 4 plus 3 cube root of 2 end root
This gives answer as a single surd. Hope this is the form you require. 

Answered by satyajit samal | 15th Jun, 2015, 11:43: AM

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