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Question
Find the square root of the following rational expression
`(7x^2 + 2sqrt(14)x + 2)/(x^2 - 1/2 x + 1/16)`
Solution
`sqrt((7x^2 + 2sqrt(14) x + 2)/(x^2 - 1/2 x + 1/16)`
= `sqrt(((sqrt(7)x)^2 + 2 xx sqrt(7)x xx sqrt(2) +(sqrt(2))^2)/(x^2 - 2 xx x xx 1/4 + (1/4)^2)`
= `sqrt((sqrt(7)x + sqrt(2))^2/(x - 1/4)^2)`
= `|(sqrt(7)x + sqrt(2))/(x - 1/4)|`
or
= `4|(sqrt(7)x + sqrt(2))/(4x - 1)|`
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