How do you rationalize the denominator $(sqrt27-sqrt7)/(sqrt21-3)$ ?

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Answer 1 · 2018-03-24T03:28:16

$(sqrt27-sqrt7)/(sqrt21-3)$

Multiply both the numerator and denominator with $(sqrt21+3)$ ,

$(sqrt27-sqrt7)/(sqrt21-3)xx(sqrt21+3)/(sqrt21+3)$

Apply difference of two squares rule,

$((sqrt27-sqrt7)(sqrt21+3))/(sqrt21^2-3^2)$

Expand,

$((sqrt27)(sqrt21)+(-sqrt7)(sqrt21)+(sqrt27)(3)+(-sqrt7)(3))/(21-9)$

Simplify,

$(6sqrt7+2sqrt3)/12$

SImplest form,

$(3sqrt7+2sqrt3)/6$

How do you rationalize the denominator (sqrt27-sqrt7)/(sqrt21-3)(sqrt27-sqrt7)/(sqrt21-3)?