Question 221155
I have an equation (2x^2)-7=0. The answer I have been given is the square root of 14 over 2. I'm unsure why. Could you walk me through the steps please?


{{{2x^2 - 7 = 0}}}


{{{2x^2 = 7}}} ------- Adding 7 to both sides of equation


{{{(2x^2)/2 = 7/2}}} ------- Dividing both sides of equation by 2


{{{x^2 = 7/2}}}


{{{sqrt(x^2) = sqrt(7/2)}}} ----- {{{x^2 = sqrt(7)/sqrt(2)}}}

This could be the answer, but since you have a different answer, it's quite obvious that they want you to RATIONALIZE the denominator (not leaving the denominator with a square root value).


So, {{{x^2 = sqrt(7)/sqrt(2)}}} 


{{{x^2 = (sqrt(7)*sqrt(2))/(sqrt(2)*sqrt(2))}}} ------ Rationalizing denominator


Therefore, we get: {{{x^2 = sqrt(7*2)/2}}}, or: {{{highlight_green(sqrt(14)/2)}}}