Is the equation true or LHS = RHS ?

`sqrt1 + sqrt1 = sqrt2 `

Can the direction cosines of a line be 1/sqrt2 , 1/sqrt2, 1/sqrt2 ?

If sqrt2 = 1.4142 , find the value of 2sqrt2 + sqrt2 + (1)/(2 + sqrt2) + (1)/(sqrt2 - 2)

The sum of the series 1/(sqrt2 + sqrt1) + 1/(sqrt2 + sqrt3) + ……+ 1/ (sqrt120 + sqrt121) is .

Use the principle of mathematical induction to prove that for all n in N sqrt(2+sqrt(2+sqrt2+...+...+sqrt2))=2cos ((pi)/(2^(n+1))) When the LHS contains n radical signs.

Use induction to show that for all n in N . sqrt(a+sqrt(a+sqrt(a+....+sqrt(a))))lt (1+sqrt((4a+1)))/(2) where'a' is fixed positive number and n radical signs are taken on LHS.

The value of { 1/(sqrt6 - sqrt5) - 1/(sqrt5 - sqrt4) + 1/(sqrt4 - sqrt3) - 1/(sqrt3 - sqrt2) + 1/(sqrt2 - 1)} is :