Question

Needs help understanding how to solve this question! It really confuses me! sqrt(c)-sqrt(d)/sqrt(c)+sqrt(d)

Answer 1

one problem is that is isn't an equation as the statement isn't equal to anything

Answer 2

Ok the instructions say to rationalize the denominator. Assume all expressions under radicals represent positive numbers.

Answer 3

When you have a sum of square roots on the bottom, you can multiply the bottom by the conjugate... Multiply the top and bottom by sqrt(c) - sqrt(d) to get the answer.

Answer 4

so I am multiplying and one will cancel out and since I am multiply by sqrt(c)-sqrt(d) the top cancels?

Answer 5

rationalising the denominator means multiplying by something that will give a rational number....

you always multiply by 1 which is written in another form

in your question use the denominator with the opposite sign

\[1 = (\sqrt{c} - \sqrt{d})/(\sqrt{c} -\sqrt{d})\]

so the problem is now

\[(\sqrt{c} - \sqrt{d})/(\sqrt{c} + \sqrt{d}) \times (\sqrt{c} - \sqrt{d})/(\sqrt{c} - \sqrt{d})\]

this simplifies to
\[(\sqrt{c} - \sqrt{d})^2 /(c - d)\]

the radicals are removed from the denominator

Answer 6

Ok...I see now...thanks so much!

Answer 7

One more question...when typing in my answer, are the ( ) needed?