1/(5+sqrt(6)) is equal to about .134237
You rationalize denominators by using a form of one. Thus. sqrt(X + 6)/sqrt(X) * sqrt(X)/sqrt(X) = sqrt(X2 + 6X)/X ------------------------
11*sqrt(8) + 6*sqrt(12) - 5*sqrt(2) = 11*sqrt(4*2) + 6*sqrt(4*3) - 5*sqrt(2) = 11*sqrt(4)*sqrt(2) + 6*sqrt(4)*sqrt(3) - 5*sqrt(2) = 11*2*sqrt(2) + 6*2*sqrt(3) - 5*sqrt(2) = 22*sqrt(2) - 5*sqrt(2) + 12*sqrt(3) = 17*sqrt(2) + 12*sqrt(3) and that cannot be simplified further.
sqrt(24) = sqrt(4*6) = sqrt(4)*sqrt(6) = 2*sqrt(6)
sqrt(54) = sqrt(9*6) = sqrt(9)*sqrt(6) = 3*sqrt(6)
6*sqrt(50) + 6*sqrt(2) = 6*sqrt(25*2) + 6*sqrt(2) = 6*sqrt(25)*sqrt(2) + 6*sqrt(2) = 6*5*sqrt(2) + 6*sqrt(2) = 30*sqrt(2) + 6*sqrt(2) = 32*sqrt(2)
sqrt(24) + sqrt(54) = sqrt(4*6) + sqrt(9*6) = sqrt(4)*sqrt(6) + sqrt(9)*sqrt(6) = 2*sqrt(6) + 3*sqrt(6) = 5*sqrt(6) That is probably the answer required. But a moment with a calculator will show that this is 12.247 (approx).
[The sqrt(3)+sqrt(2)]/sqrt(6)can be solved by multiply the numerator and denominator by sqrt(6)This gives sqrt(18)+sqrt(12)/6This can be simplified to[3(sqrt(2)+2(sqrt(3)]/6
x = [-6 +/- sqrt(62-4*1*41)]/2 =[-6 +/- sqrt(36-164)]/2 =[-6 +/- sqrt(-128)]/2 = -3 +/- sqrt(-32) = -3 +/- i*sqrt(32) where i = the imaginary sqrt of -1
1/(5+sqrt(6)) is equal to about .134237
It is sqrt(3)*[1 + sqrt(2)]/3 or [1 + sqrt(2)]/sqrt(3)
You rationalize denominators by using a form of one. Thus. sqrt(X + 6)/sqrt(X) * sqrt(X)/sqrt(X) = sqrt(X2 + 6X)/X ------------------------
x=(6±sqrt(36-4*6))/2 x=3±(sqrt(12)/2) x=3±sqrt(3)
11*sqrt(8) + 6*sqrt(12) - 5*sqrt(2) = 11*sqrt(4*2) + 6*sqrt(4*3) - 5*sqrt(2) = 11*sqrt(4)*sqrt(2) + 6*sqrt(4)*sqrt(3) - 5*sqrt(2) = 11*2*sqrt(2) + 6*2*sqrt(3) - 5*sqrt(2) = 22*sqrt(2) - 5*sqrt(2) + 12*sqrt(3) = 17*sqrt(2) + 12*sqrt(3) and that cannot be simplified further.
2 sqrt(6) - 5 sqrt(24) = 2 sqrt(6) - 5 sqrt(4 x 6) = 2 sqrt(6) - 5 sqrt(4) sqrt(6) =2 sqrt(6) - 5 x 2 sqrt(6) = 2 sqrt(6) - 10 sqrt(6) =-8 sqrt(6)
Because questions can't use punctuation the question is ambiguous. Two possible interpretations of the question, with answers are given below:sqrt(3) + sqrt(6) / sqrt(2) = sqrt(3) + sqrt(6/2) = sqrt(3) + sqrt(3) = 2*sqrt(3)The more likely question is:[sqrt(3) + sqrt(6)]/sqrt(2)Multiply numberator and denominator by sqrt(2) to give[sqrt(2)*sqrt(3) + sqrt(2)*sqrt(6)]/[sqrt(2)*sqrt(2)]=[sqrt(2)*sqrt(3) + 2*sqrt(3)]/2 since sqrt(2)*sqrt(2) = 2= sqrt(3)*[sqrt(2)+1]/2AnswerSquare root three plus square root six is square root 9 over square root two. But nine can be factored out to a perfect three so you would have 3 over square root two.
Sqrt of 200+(6*20) = 134.1421356