Rationalize the denominator (√2+√5)/(√3-√7).

[kacymindy]

Rationalize the denominator (√2+√5)/(√3-√7).

I got this as the answer, - (√2+√5)(√3+√7)/(4).

Is this correct or do I have to multiply it using the foil method and get this? -(√6+√14+√15+√35))/(4).

So is either answer okay and can I stick with my first answer?

 

[Deleted member 4993]

Rationalize the denominator (√2+√5)/(√3-√7).

I got this as the answer, - (√2+√5)(√3+√7)/(4).

Is this correct or do I have to multiply it using the foil method and get this? -(√6+√14+√15+√35))/(4).

So is either answer okay and can I stick with my first answer?

In my opinion you finished the problem (did what you were asked to do) in the second line and you are good!!

 

[Steven G]

Factored form is always best.

 

[JeffM]

Rationalize the denominator (√2+√5)/(√3-√7).

I got this as the answer, - (√2+√5)(√3+√7)/(4).

Is this correct or do I have to multiply it using the foil method and get this? -(√6+√14+√15+√35))/(4).

So is either answer okay and can I stick with my first answer?

Both your results are correct and identical in meaning. There are many ways to show the answer. For example,

[MATH]-\ \dfrac{\sqrt{2} + \sqrt{5}}{2} * \dfrac{\sqrt{3} + \sqrt{7}}{2}.[/MATH]
So you are really asking a question about what is conventional in presentation. The seemingly childish answer to that question is that you should do whatever your teacher requires, no matter how absurd: there is nothing to be gained by arguing with stupid authority over the immaterial. In general, however, I agree with jomo: most would prefer showing the factored form in your second line.

 

[lookagain]

Rationalize the denominator (√2+√5)/(√3-√7).

There are many ways to show the answer. For example,

− √2+√52∗√3+√72.− 2+52∗3+72.

This would not be an acceptable way to show the answer, because the instructions are to "rationalize the (singular)
denominator."

 

[Deleted member 4993]

Much ado about nothing....

Tempest in a Kuereg coffee maker....