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Question
Compare the following pair of ratios.
`(3sqrt5)/(5sqrt7) , sqrt 63 / sqrt 125`
Solution
`3sqrt5 xx sqrt 125 = 3sqrt5 xx sqrt (25 xx 5) = 3sqrt5 xx 5sqrt5 = 75`
`5sqrt7 xx sqrt63 = 5sqrt7 xx sqrt ( 9 xx 7) = 5sqrt7 xx 3sqrt7 = 105`
Now, 75 < 105
`therefore (3sqrt5)/(5sqrt7) < sqrt 63/ sqrt 125`.
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