`(sqrt? - 1)^2=8-sqrt28`

(sqrt(x)-1)^(2)=8-sqrt(28) find the value of x

sqrt 2(sqrt 2+1) - sqrt 2 (1+sqrt2) =?

Show that : (1)/(3-2sqrt(2))- (1)/(2sqrt(2)-sqrt(7)) + (1)/(sqrt(7)-sqrt(6))-(1)/(sqrt(6)-sqrt(5))+(1)/(sqrt(5)-2)=5 .

Rationalize the denominator: (2 + sqrt 3)/(2 - sqrt 3) + (2 - sqrt 3)/(2 + sqrt 3) + (sqrt 3 - 1)/(sqrt 3 + 1)

Evaluate : (1)/(3-sqrt(8)) -(1)/(sqrt(8)-sqrt(7))+(1)/(sqrt(7)-sqrt(6))-(1)/(sqrt(6)-sqrt(5))+(1)/(sqrt(5)-2).

FOIL (sqrt8-sqrt2)(sqrt8-sqrt2)

Find (sqrt3 - sqrt 2)/(sqrt 3+sqrt 2) -(sqrt3 + sqrt 2)/(sqrt 3-sqrt 2) +1/(sqrt2+1)-1/(sqrt2-1)

(sqrt(3)-sqrt(2))/(sqrt(3)+sqrt(2))-(sqrt(3)+sqrt(2))/(sqrt(3)-sqrt(2))+(1)/(sqrt(2)+1)-(1)/(sqrt(2)-1)

STATEMENT-1 : The length of latus rectum of the parabola (x - y + 2)^(2) = 8sqrt(2){x + y - 6} is 8sqrt(2) . and STATEMENT-2 : The length of latus rectum of parabola (y-a)^(2) = 8sqrt(2)(x-b) is 8sqrt(2) .

Prove that tan 7 (1^(@))/(2) = sqrt2 - sqrt3 -sqrt4 + sqrt6 = (sqrt3 - sqrt2) (sqrt2 -1).