Rationalize the denominator.

Question

anonymous · Answer

he bottom of a fraction is called the denominator. 
Numbers like 2 and 3 are rational.
But many roots, such as √2 and √3, are irrational.

mathstudent55 · Answer

Where is the question?

nsh4267 · Answer

$$\frac{ \sqrt{t} +8}{ \sqrt{t}-8 }$$

mathstudent55 · Answer

Do you know the product of a sum and a difference?

$(a + b)(a - b) = a^2 - b^2 $

nsh4267 · Answer

(x+y)(x-y)

mathstudent55 · Answer

Right.
To rationalize a denominator, you need to get rid of all roots in the denominator.

nsh4267 · Answer

t-64

mathstudent55 · Answer

Notice that when you multiply a sum and a difference of two numbers, the result is the difference of the squares of the two numbers. There is no middle term, like in the squaring of a binomial.

mathstudent55 · Answer

For exqmple,

$(\sqrt{x} + 2) (\sqrt{x} - 2) = (\sqrt{x})^2 - (2)^2 = x - 4$

Notice that there was a square root, but after the multiplication, there is no longer a square root.

mathstudent55 · Answer

You need to do a similar thing to your denominator.
You have a difference in the denominator.
What is the sum that you need to multiply the denominator by to have a product of a sum and a difference and to eliminate the square root of the denominator?

phi · Answer

multiply top and bottom by 
$$ \sqrt{t}+8$$

nsh4267 · Answer

$$t+8\sqrt{t}+8\sqrt{t}+64$$

nsh4267 · Answer

$$t+16\sqrt{t}+64$$

phi · Answer

the bottom becomes  t-64
I would leave the top as  (sqr(t) +8)^2
$$ \frac{ (\sqrt{t} +8)^2}{t-64} $$

nsh4267 · Answer

all over t-64

phi · Answer

if it's multiple choice, you might have to expand the top.. it depends how they give the choices.

phi · Answer

yes, if you multiply it out, that is what you get.