Rationalizing the Denominator

Rationalize the denominator means to convert the denominator containing square root term into a rational number by finding the equivalent fraction of the given fraction.

For which we can use the identities of the real numbers.

Example:

Rationalize the denominator of \dfrac{7}{(7-\sqrt3)} .

Solution:

\dfrac{7}{7-\sqrt3}\times\dfrac{7+\sqrt3}{7+\sqrt3}=\dfrac{7(7+\sqrt3)}{49-3}=\dfrac{49+7\sqrt3}{46}

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