Question

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

Answer 1

Answer:

Here is the answer of the above question

Answer 2

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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