# How do you rationalise the denominator of #8/(3-sqrt5)#?

Multiply both numerator and denominator by

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To rationalize the denominator of ( \frac{8}{3 - \sqrt{5}} ), you multiply both the numerator and denominator by the conjugate of the denominator. In this case, the conjugate of (3 - \sqrt{5}) is (3 + \sqrt{5}).

So, we multiply both the numerator and the denominator by (3 + \sqrt{5}):

[ \frac{8}{3 - \sqrt{5}} \times \frac{3 + \sqrt{5}}{3 + \sqrt{5}} ]

Expanding the numerator and the denominator, we get:

[ \frac{8(3 + \sqrt{5})}{(3 - \sqrt{5})(3 + \sqrt{5})} ]

[ = \frac{24 + 8\sqrt{5}}{9 - 5} ]

[ = \frac{24 + 8\sqrt{5}}{4} ]

[ = 6 + 2\sqrt{5} ]

So, ( \frac{8}{3 - \sqrt{5}} ) rationalizes to ( 6 + 2\sqrt{5} ).

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