`(sqrt 7 - sqrt 5)^2- (sqrt 7 + sqrt 5)^2`

Rationalize the denominator 1/(sqrt 3 - sqrt 2) - 2/(sqrt 5 - sqrt 3) + 3/(sqrt 5 - sqrt 2)

Simplify {(\sqrt 5+\sqrt 3)\times (\sqrt 5 - \sqrt 3)}/(\sqrt 7- \sqrt 3)\times (\sqrt 7+ \sqrt 3)/(\sqrt 7+\sqrt 3)

2sqrt5 - sqrt5 = sqrt5

Prove that: 1/(3-sqrt(8))-1/(sqrt(8)-\ sqrt(7))+1/(sqrt(7)-\ sqrt(6))-1/(sqrt(6)-\ sqrt(5))+1/(sqrt(5)-2)=5

Find the number of terms in the following expansions. ( sqrt(3) + sqrt(5) )^(7) ( sqrt(3) - sqrt(5) )^(7)

If sqrt (7 sqrt (7 sqrt7 sqrt7 sqrt7)) = 7 ^(x) then find the value of x

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

Simplify each of the following : (i)(sqrt(2)+1)/(sqrt(2)-1)+(sqrt(2)-1)/(sqrt(2)+1)" "(ii)(sqrt(5)+sqrt(3))/(sqrt(5)-sqrt(3))+(sqrt(5)-sqrt(3))/(sqrt(5)+sqrt(3))" "(iii)(2)/(sqrt(5)+sqrt(3))+(1)/(sqrt(3)+sqrt(2))-(3)/(sqrt(5)+sqrt(2))" "(iv)(sqrt(7)+sqrt(5))/(sqrt(7)-sqrt(5))-(sqrt(7)-sqrt(5))/(sqrt(7)+sqrt(5))

{:(sqrt(5)x - sqrt(7)y = 0),(sqrt(7)x - sqrt(3)y = 0):}

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