1 Application and 1 Rationalizing Denominator - Need Help

[Gent]

1. The number of households h, in millions, served by cable television at a point in time x years after 1970 can be modeled by the function below:

. . . . .\(\displaystyle h(x)\, =\, 11.7994\, +\, \sqrt{\strut 172.7948x\, -\, 1719.9421\,}\)

Use h (x ) to estimate the number of households served by cable television in 1984.

My question: How do I find x?

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2. Rationalize the denominator, and simplify:

. . . . .\(\displaystyle \dfrac{\sqrt{\strut 5\,}\, -\, \sqrt{\strut 2\,}}{\sqrt{\strut 2\,}\, -\, \sqrt{\strut 5\,}}\)

My question: I tried multiplying by the conjugate but that doesn't get rid of the radical...Please help me solve.

 

[Deleted member 4993]

1. The number of households h, in millions, served by cable television at a point in time x years after 1970 can be modeled by the function below:

. . . . .\(\displaystyle h(x)\, =\, 11.7994\, +\, \sqrt{\strut 172.7948x\, -\, 1719.9421\,}\)

Use h (x ) to estimate the number of households served by cable television in 1984.

My question: How do I find x?

How many years after 1970 does 1984 come up?

2. Rationalize the denominator, and simplify:

. . . . .\(\displaystyle \dfrac{\sqrt{\strut 5\,}\, -\, \sqrt{\strut 2\,}}{\sqrt{\strut 2\,}\, -\, \sqrt{\strut 5\,}}\)

My question: I tried multiplying by the conjugate but that doesn't get rid of the radical...

Please show work