Question

`(4)/(sqrt(10-2sqrt(21)))`=______.
A. `(1)/(4)(sqrt(7)+sqrt(3))`
B. `(1)/(4)(sqrt(7)-sqrt(3))`
C. `sqrt()7+sqrt()3`
D. `sqrt(7)+sqrt(3)`

Answer 1

Correct Answer - C
`(4)/(sqrt(10-2sqrt(21)))=(4)/(sqrt((sqrt(7))^(2)+(sqrt(3))^(2)-2sqrt(7xx3)))`
`=(4)/(sqrt((sqrt(7)-sqrt(3))^(2)))=(4)/(sqrt(7)-sqrt(3))`
`(4(sqrt(7)+sqrt(3)))/((sqrt(7)-sqrt(3))(sqrt(7)+sqrt(3)))`
`(4(sqrt(7)+sqrt(3)))/(4)=sqrt(7)+sqrt(3)`