Question

If `sqrt(0.04 xx 0.4 xx a ) = 0.4 xx0.04 xx sqrtb` then find the ratio `a/b`.

Answer 1

`sqrt(0.04 xx 0.4 xx a ) = 0.4 xx0.04 xx sqrtb`
⇒ `sqrt( 0.04 xx 0.4) xx sqrta` = 0.4 x 0.04 x `sqrtb`
⇒ `sqrta/sqrtb = (sqrt {0.4 xx 0.04}  )^2/( 0.4 xx 0.04 )`
⇒ `sqrt(a/b) = sqrt( 0.4 xx 0.04 )`
⇒ `a/b = 0.4 xx 0.04`
⇒ `a/b = 4/10 xx 4/100 = 16/1000`
⇒ `a/b = 2/125`
`therefore` a : b = 2 : 125