`(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)

2sqrt5 - sqrt5 = sqrt5

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

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

{:(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 ).

Find the values of a and b in each of the following : (a)(5+2sqrt3)/(7+4sqrt(3))=a-6sqrt(3)" "(b)(3-sqrt(5))/(3+2sqrt(5))=asqrt(5)-(19)/(11) (c )(sqrt(2)+sqrt(3))/(3sqrt2-2sqrt(3))=2-bsqrt(6)" "(d)(7+sqrt(5))/(7-sqrt(5))-(7-sqrt(5))/(7+sqrt(5))=a+(7)/(11)sqrt(5b)

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

(sqrt(7)+2sqrt(3))(sqrt(7)-2sqrt(3))

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