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How do you rationalize the denominator #(sqrt2)/(sqrt7+3)#?

Answer 1

Eva Adamson

Multiply the numerator and the denominator by #sqrt7 -3# to have #(sqrt14 -3sqrt2)/(7-9)#

=#(sqrt14 -3sqrt2)/(-2)#

=#(3sqrt2-sqrt14)/2#

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Answer 2

Eva Adamson

To rationalize the denominator of the expression (sqrt2)/(sqrt7+3), we can multiply both the numerator and denominator by the conjugate of the denominator, which is (sqrt7-3). This will eliminate the square root in the denominator.

By applying the conjugate, the expression becomes (sqrt2)/(sqrt7+3) * (sqrt7-3)/(sqrt7-3).

Multiplying the numerators and denominators, we get (sqrt2 * sqrt7 - sqrt2 * 3) / ((sqrt7 + 3) * (sqrt7 - 3)).

Simplifying further, we have (sqrt(2 * 7) - 3sqrt2) / (7 - 3^2).

This simplifies to (sqrt14 - 3sqrt2) / (7 - 9), which further simplifies to (sqrt14 - 3sqrt2) / (-2).

Therefore, the rationalized form of the expression (sqrt2)/(sqrt7+3) is (sqrt14 - 3sqrt2) / (-2).

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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.