SOLUTION: can you please help me solve the following and express irrational solutions in simplest radical form: ((( (n-5)^2=20 )))

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: can you please help me solve the following and express irrational solutions in simplest radical form: ((( (n-5)^2=20 )))      Log On


   

Question 197967This question is from textbook algebra sturcture and method
: can you please help me solve the following and express irrational solutions in simplest radical form: ((( (n-5)^2=20 ))) This question is from textbook algebra sturcture and method

Found 2 solutions by solver91311, jim_thompson5910:
Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!




Take the square root of both sides, considering both the positive and negative square roots:



Solve for the variable:



Find the prime factorization of the radicand:



There are two factors of 2 in the radicand. Eliminate them and take one of them outside:



So:



John

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

%28n-5%29%5E2=20 Start with the given equation.


x-5=%22%22%2B-sqrt%2820%29 Take the square root of both sides.


n-5=sqrt%2820%29 or n-5=-sqrt%2820%29 Break up the "plus/minus" to form two equations.


n-5=2%2Asqrt%285%29 or n-5=-2%2Asqrt%285%29 Simplify the square root.


n=5%2B2%2Asqrt%285%29 or n=5-2%2Asqrt%285%29 Add 5 to both sides.


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Answer:


So the solutions are n=5%2B2%2Asqrt%285%29 or n=5-2%2Asqrt%285%29.