Question

How do you solve roots and radical questions that have fractions underneath the radical sign? For example the following question: 1/2√4/3 - 2/3√3/4 + 2√1/12

Answer 1

Let us look at the posted question step by step,

`1/2sqrt{4/3}+2/3sqrt{3/4}+2sqrt{1/12}`

by distributing the square-roots to the numerator and the denominator,

`=1/2 sqrt{4}/sqrt{3}+2/3sqrt{3}/sqrt{4}+2sqrt{1}/sqrt{12}`

by multiplying the numerator and the denominator by the denominator to rationalize the denominators,

`=1/2 {sqrt{4}cdot sqrt{3}}/{sqrt{3}cdot sqrt{3}}+2/3{sqrt{3}cdot sqrt{4}}/{sqrt{4}cdot sqrt{4}}+2{sqrt{1}cdot sqrt{12}}/{sqrt{12}cdot sqrt{12}}`

by simplifying a bit further,

`=1/6sqrt{12}+1/6 sqrt{12}+1/6sqrt{12}`

by `sqrt{12}=2sqrt{3}`,

`=\frac{1}{3}sqrt{3}+\frac{1}{3}sqrt{3}+\frac{1}{3}sqrt{3}`

by factoring out `sqrt{3}`,

`=(1/3+1/3+1/3)sqrt{3}=sqrt{3}`

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I hope that this was helpful.