y varies directly with square root of x and y =9 when x =9 . Find the value of x when y =6 .

Explanation

As per question , ` y prop sqrt(x) rArr y=k sqrt(x)……..(1)` (where k = non -zero variation constant )
When x =9 , y =9 `therefore 9=ksqrt(9) [by(1)]`
or , 9= k.3 or k=`9/3=3`.
`therefore "from" (1) we "get" , y=3 sqrt(x) ……….(2)`
Now ,when y=6 from (2) we get , 6 =`3sqrt(x)`
or , `sqrt(x) =6/3=2 `
or, x =`(2)^(2)` =4 [Squaring both the sides ]
`therefore` The required value of x =4 .