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How do you rationalize #4/(6-sqrt7)#?

Answer 1

Julia Adams

Multiply both numerator and denominator by #(6 + sqr7)#

#[4(6 + sqr7)]/(36 - 7)# = #[4(6 + sqr7)]/29#

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Answer 2

Eva Adamson

To rationalize the expression 4/(6-sqrt7), we can multiply both the numerator and denominator by the conjugate of the denominator, which is 6+sqrt7. This will eliminate the square root in the denominator.

By applying the conjugate, the expression becomes (4 * (6+sqrt7))/((6-sqrt7) * (6+sqrt7)).

Simplifying further, we get (24+4sqrt7)/(36-7).

This simplifies to (24+4sqrt7)/29.

Therefore, the rationalized form of 4/(6-sqrt7) is (24+4sqrt7)/29.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.