Basic surds

[badvibes]

Simplify:

[MATH](7+\sqrt3)(5-\sqrt3)[/MATH]
So I use FOIL:

[MATH]=35-7\sqrt3+5\sqrt3+3[/MATH]
[MATH]=38-2\sqrt3[/MATH]
I have also tried to fumble through by swapping the + and - to no avail. Something basic and rather important is totally lost on me here.

Message to admins/moderators: This is my second account because I lost my previous email and password. Username was clownshoes I believe. Thank you for all the help you've provided in the past.

 

[tkhunny]

What do you perceive to be the problem? Positive * Negative gives what?

 

[HallsofIvy]

\(\displaystyle (\sqrt{3})(-\sqrt{3})= -3\), not 3.

 

[Steven G]

Why is 7(-√3) = -7√3 but √3(-√3) = +3? You need to be consistent with the signs!

 

[badvibes]

Thank you all very kindly for your input. However on this online learning facility the questions randomise, I have now been generated a new similar question. All my methods have been foiled.

Simplify:

[MATH](5+\sqrt6)(2-\sqrt6) [/MATH]
So I've began:

[MATH]=10-5\sqrt6+2\sqrt6-6[/MATH]
[MATH]=4-3\sqrt6[/MATH]
Incorrect, so I switched the -+ but I stayed consistent (I believe)

[MATH]=10+5\sqrt6-2\sqrt6-6[/MATH]
[MATH]=4+3\sqrt6[/MATH]
It is not the correct answer either.

I am obviously ashamed to be stumped at this problem but I cannot see where I am making the error.

Please can you continue to advise me on where I am going wrong. Thank you.

 

[HallsofIvy]

In a bit more detail: \(\displaystyle (\sqrt{3})(-\sqrt{3})= (\sqrt{3})(-1)(\sqrt{3})= (-1)(\sqrt{3})(\sqrt{3})= (-1)(3)= -3\).

 

[MarkFL]

Thank you all very kindly for your input. However on this online learning facility the questions randomise, I have now been generated a new similar question. All my methods have been foiled.

Simplify:

[MATH](5+\sqrt6)(2-\sqrt6) [/MATH]
So I've began:

[MATH]=10-5\sqrt6+2\sqrt6-6[/MATH]
[MATH]=4-3\sqrt6[/MATH]
Incorrect, so I switched the -+ but I stayed consistent (I believe)

[MATH]=10+5\sqrt6-2\sqrt6-6[/MATH]
[MATH]=4+3\sqrt6[/MATH]
It is not the correct answer either.

I am obviously ashamed to be stumped at this problem but I cannot see where I am making the error.

Please can you continue to advise me on where I am going wrong. Thank you.

Your first attempt was in fact correct.

 

[badvibes]

Your first attempt was in fact correct.

Thank you.

 

[Steven G]

If 4−3√6 was not accepted I would try −3√6+4 as your answer is correct.

 

[badvibes]

If 4−3√6 was not accepted I would try −3√6+4 as your answer is correct.

Very good idea.

It generated me another problem which I solved with the help you've given me and, unfortunately, it did not matter. Thank you for the lesson.