`(6+sqrt7)(5+sqrt5)`

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

Multiply 6sqrt(5) by 2sqrt(5) .

State, whether the following numbers are rational or not : (i) (2+sqrt(2))^(2)" (ii) "(5+sqrt(5))(5-sqrt(5)) (iii) (sqrt(7)/(5sqrt(2)))^(2)

((4 +sqrt5)/(4-sqrt5)) +((4-sqrt5)/(4+sqrt5)) =?

If center of a regular hexagon is at the origin and one of the vertices on the Argand diagram is 1+2i , then its perimeter is 2sqrt(5) b. 6sqrt(2) c. 4sqrt(5) d. 6sqrt(5)

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

Simplify the following expressions. (i) (5+sqrt(7))(2+sqrt(5)) (ii) (5+sqrt(5))(5-sqrt(5)) (iii) (sqrt(3)+sqrt(7))^2 (iv) (sqrt(11)-sqrt(7))(sqrt(11)+sqrt(7))

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))

Simplify (5+sqrt(7))(5+sqrt(2))

Write in ascending order: 6 sqrt(5) , 7 sqrt(3) and 8 sqrt(2)