Math, asked by MohdZabeeh, 8 months ago

Rationalize the denominator of 6−√5 6+√5

Answers

Answered by Amarjeet2534
5

Answer:

Here is the answer of the above question

Attachments:
Answered by halamadrid
5

The correct answer is \frac{41-12\sqrt{5} }{31} .

Given:

(6−√5)/(6+√5).

To Find:

The rationalization of (6−√5)/(6+√5).

Solution:

By rationalizing a given fraction, we remove the root in the denominator.

To rationalize fractions with denominators of the form 'x+y' we will multiply the conjugate of the denominator 'x-y' to both the numerator and the denominator.

The denominator of the given fraction is (6+√5). It conjugate = (6-√5).

Multiplying (6-√5) to both the numerator and the denominator of the given fraction, we have:

\frac{(6-\sqrt{5} )}{(6+\sqrt{5} )} x \frac{(6-\sqrt{5} )}{(6-\sqrt{5} )} = \frac{(6-\sqrt{5})^{2}  }{(6+\sqrt{5})(6-\sqrt{5})} = \frac{6^{2} -2(6)(\sqrt{5}) +\sqrt{5}^{2}  }{(6^{2}-\sqrt{5}^{2})} = \frac{36-12\sqrt{5}+5 }{36-5} = \frac{41-12\sqrt{5} }{31}

Hence, on the rationalization of (6−√5)/(6+√5), we obtain  \frac{41-12\sqrt{5} }{31} .

The correct answer is \frac{41-12\sqrt{5} }{31} .

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