Question

Rationalize the denominator and simplify

Answer 1

`\frac{22}{4 - \sqrt {5}} * \frac{4 + \sqrt {5}}{4 + \sqrt {5}} =`


`= \frac{22(4 + \sqrt {5})}{16 - 5}`


`= \frac{22(4 + \sqrt {5})}{11}`


`= 2(4 + \sqrt {5})`


`= 8 + 2\sqrt {5}`

Answer 2

22 x (4+√5)
_____ _______
(4-√5) (4+√5) Multiply by the conjugate of the denominator.

= 88 + 22√5 = 88 + 22√5 = 11(8+2√5) = 8+2√5
____________ _________ _________

16+4√5-4√5-5 11 11


Answer: 8 + 2√5

Hope this helps :)