Algebra 1 11.9b - Conjugates

Conjugates in expressions involving radicals; using conjugates to simplify expressions.

Category:

Education

Tags:

• Algebra 1
• algebra
• conjugate
• conjugates
• radical
• radicals
• radical expression
• radical expressions
• homeschool
• distance learning
• Derek Owens

[lkkoller]

At 3:10 you say a and b can be any numbers. You "prove" the idea for any a and b. If you let b = sqrt(2), then plugging in to your (a+sqrt(b)) * (a - sqrt(b)) you would have (a + sqrt(sqrt(2)) * (a - sqrt(sqrt(2)) which equals a^2 + sqrt(2), which DOES NOT eliminate the radical. I just don't understand this at all.

[derekowens]

@lkkoller Actually I think that will work. If you have (a + sqrt(sqrt(2)) * (a - sqrt(sqrt(2)), when you multiply that you don't just square each term. You have to do a FOIL, and the OUTER radical will be eliminated. You will be left with a^2 - sqrt(2), and one of the radicals is gone.

[frostwow]

but what if its a one dimension higher expression in the denominator? is there still a conjugate law for that? for ex.

number +/- 2ndroot(something) +/- 3rdroot(other something)

that would be so much more fun

[derekowens]

@frostwow Yes, that would still work. The "outer" and "inner" terms would still cancel out. The last term would simply be the product, which may be a fractional exponent.

[fafase]

Knowing the a square-b rule, are we allowed to skip the FOIL and get to the answer right away when possible mentally or do we need to demonstrate it all the time?

[derekowens]

@fafase Yes, mental math and quick shortcuts are usually appropriate and helpful. Just make sure you use them only where they apply or they might lead you astray.

[tangiblephoton]

I love your accent!

[chrisrulz333]

u are defently a better teacher than i have

[frostwow]

@derekowens

[a^2 - sqrt(2)]*[a^2 + sqrt(2)] = a^4 [+ this eliminates] - 2

maths is funny business

hey derek i learnt this from you!

[Heatseaker19]

Sweet. Excellent review.

[hlgaflac]

thanks bro