Question

Following equation (see Reply), Is there an better method work or process to figuring it out? This has a solution, But I am looking for better&simpler methodologies and processes to get the solution. Keep answer as an irrational Fraction

Answer 1

\[\sqrt{\frac{ 11 }{ 2 } - 3\sqrt{2}}\] \[\sqrt{ (\frac{ 2 }{ 2 } + \frac{ 9 }{ 2 }) - 3\sqrt{2} } = \sqrt{ (\frac{ 2 }{ 2 } + \frac{ 9 }{ 2 }) - \frac{6}{2}\sqrt{2} } \] \[\sqrt{ (\frac{ 2 }{ 2 } + \frac{ 9 }{ 2 }) - \frac{3}{2}\sqrt{2} - \frac{3}{2}\sqrt{2} } = \sqrt{\frac{2}{2} + ((-)\frac{3}{2})^{2} - \frac{3}{2}\sqrt{2} - \frac{3}{2}\sqrt{2}} \] Then \[\sqrt{\frac{ 11 }{ 2 } - 3\sqrt{2}}\ =1+ \frac{ 3 }{ 2 }\sqrt{2}\]

Im having issues getting the middle part and figuring if there is an easier method to figuring this out.

Answer 2

\[\LARGE{\sqrt{5.5-3\sqrt{2}}}\]

Answer 3

\[\sqrt{5.5-3(1.414)}\]

Answer 4

not sure but i think it can make easy the solution :)

Answer 5

Nah, as I said in the equation
\[\sqrt{\frac{ 11 }{ 2 } - 3 \sqrt{2}} = 1 - \frac{ 3 }{2 }\sqrt{2}\] thus the answer is \[1 - \frac{ 3 }{2 }\sqrt{2}\] square root cancels out the exponential \[\sqrt{ (1 - \frac{ 3 }{2 }\sqrt{2})^2}\]
The answer is to be given as an irrational fraction to simplify and give more accurate result than having it in decimal .

What I am trying to better my self is in the process of solving this equation to its simplest form:

Answer 6

Also I accidentally miswrote the solution to the equation in the reply, it should be the above.

Answer 7

I guess my solution is as advance as people here can explain it. Will keep this open until I get a better solution to this