SOLUTION: can you please check if i got the right answer for this problem: 2√8+7√8/1-√2 these are my steps: 9√8/1-√2 multiplied by (1+√2/1+√2

Algebra ->  Algebra  -> Square-cubic-other-roots -> SOLUTION: can you please check if i got the right answer for this problem: 2√8+7√8/1-√2 these are my steps: 9√8/1-√2 multiplied by (1+√2/1+√2      Log On

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Question 214925: can you please check if i got the right answer for this problem: 2√8+7√8/1-√2
these are my steps:

9√8/1-√2 multiplied by (1+√2/1+√2)
9√8(1-√2)/1+2
and this is my answer: 9√8(1-√2)/3
Answer by jim_thompson5910(21685) About Me  (Show Source):
You can put this solution on YOUR website!
Unfortunately, that is not the correct answer. You can use a calculator to find the approximations of the two expressions. If the expressions are close enough approximately, then chances are they are equal. In this case, I found that

%282%2Asqrt%288%29%2B7%2Asqrt%288%29%29%2F%281-sqrt%282%29%29=-61.45584 (approximately)

and

%289%2Asqrt%288%29%2A%281-sqrt%282%29%29%29%2F3=-3.51472 (approximately)


So %282%2Asqrt%288%29%2B7%2Asqrt%288%29%29%2F%281-sqrt%282%29%29%3C%3E%289%2Asqrt%288%29%2A%281-sqrt%282%29%29%29%2F3



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To make things simpler, simplify the numerator 2%2Asqrt%288%29%2B7%2Asqrt%288%29 to get: 2%2Asqrt%288%29%2B7%2Asqrt%288%29=%282%2B7%29%2Asqrt%288%29=9%2Asqrt%288%29=9%2Asqrt%284%29%2Asqrt%282%29=9%2A2%2Asqrt%282%29=18%2Asqrt%282%29. I.e. 2%2Asqrt%288%29%2B7%2Asqrt%288%29=18%2Asqrt%282%29

So the expression %282%2Asqrt%288%29%2B7%2Asqrt%288%29%29%2F%281-sqrt%282%29%29 then becomes %2818%2Asqrt%282%29%29%2F%281-sqrt%282%29%29




%2818%2Asqrt%282%29%29%2F%281-sqrt%282%29%29 Start with the given expression.


%28%2818%2Asqrt%282%29%29%2F%281-sqrt%282%29%29%29%28%281%2Bsqrt%282%29%29%2F%281%2Bsqrt%282%29%29%29 Multiply the fraction by 1%2Bsqrt%282%29


%28%2818%2Asqrt%282%29%29%281%2Bsqrt%282%29%29%29%2F%281-sqrt%282%29%29%281%2Bsqrt%282%29%29%29 Combine the fractions.


%2818%2Asqrt%282%29%2B18%2Asqrt%282%29%2Asqrt%282%29%29%2F%281-sqrt%282%29%29%281%2Bsqrt%282%29%29%29 Distribute


%2818%2Asqrt%282%29%2B18%2A2%29%2F%281-sqrt%282%29%29%281%2Bsqrt%282%29%29%29 Multiply


%2836%2B18%2Asqrt%282%29%29%2F%281-sqrt%282%29%29%281%2Bsqrt%282%29%29%29 Rearrange the terms.


%2836%2B18%2Asqrt%282%29%29%2F%281+-+2%29 FOIL


%2836%2B18%2Asqrt%282%29%29%2F%28-1%29 Combine like terms.


-36-18%2Asqrt%282%29 Reduce.


So %2818%2Asqrt%282%29%29%2F%281-sqrt%282%29%29=-36-18%2Asqrt%282%29


=====================================================

Answer:


Since %282%2Asqrt%288%29%2B7%2Asqrt%288%29%29%2F%281-sqrt%282%29%29=%2818%2Asqrt%282%29%29%2F%281-sqrt%282%29%29 this means that


highlight%28%282%2Asqrt%288%29%2B7%2Asqrt%288%29%29%2F%281-sqrt%282%29%29=-36-18%2Asqrt%282%29%29


which is our answer.



Check: take note that

%282%2Asqrt%288%29%2B7%2Asqrt%288%29%29%2F%281-sqrt%282%29%29=-61.45584 (approximately)

and

-36-18%2Asqrt%282%29=-61.45584 (approximately)


So this verifies our answer.