How do you rationalize the denominator and simplify $6/(sqrt4-sqrt14)$ ?

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Answer 1 · 2018-03-27T14:02:17

$6/(sqrt4-sqrt14)=-3/5(sqrt4+sqrt14)$

To rationalise a surd, we multiply the denominator and numerator by its conjugate.

The conjugate of $sqrta+sqrtb$ is $sqrta-sqrtb$ .

So,

$6/(sqrt4-sqrt14)$

$=(6(sqrt4+sqrt14))/((sqrt4-sqrt14)(sqrt4+sqrt14))$

$=(6(sqrt4+sqrt14))/(4-14)$

$=6/-10(sqrt4+sqrt14)$

$=-3/5(sqrt4+sqrt14)$

How do you rationalize the denominator and simplify 6/(sqrt4-sqrt14)6/(sqrt4-sqrt14)?