(a) Find the value of `sqrt(324)/sqrt(1225)` (b) Find the value of `sqrt(4(37)/(81))` (c ) Find the value of `sqrt(0.0256)` (d) Find the value of `sqrt(52.2729)`

Explanation

(a) `sqrt(324)/(1225)=(sqrt(324))/(sqrt(1225))`
By prime factorisation method we can find `sqrt(324)` and `sqrt(1225)`
`sqrt(324) = sqrt(4xxx81)= sqrt(2xx2xx3xx3xx3xx3) =2xx3xx3=8`
`sqrt(1225)=sqrt(5xx245)=sqrt(5xx5xx49)=sqrt(5xx5xx7xx7xx)=5xx7=35`
`therefore sqrt(324)/(1225)=(18)/(35)`
(b) `sqrt(361)/(81)=(sqrt(361))/(sqrt(81))=19/9`
(c )`sqrt(0.0256)=sqrt(256)/(1000)=(sqrt(256))/(sqrt(10000))=(16)/(100)=0.16`
`therefore sqrt(0.0256)=0.16`
(d) `sqrt(52.2729)=sqrt(522729)/(10000)=(sqrt(522729))/(sqrt(10000))`
Now we fund the square root of 522729 by the division method
`sqrt(522729)=723` and `sqrt(10000)=100`
`therefore sqrt(52.2729)=sqrt(522729)/(10000)=sqrt(522729)/(10000)=(723)/(100)=7.23`