help

[cvandoren]

im having problems with a couple quadratics!


8 radical 5 - 2 radical 45

Heres what I got so far:

8 Radical 5 can be reduced to 2 radical 5

Now im stuck!

heres my other one that i have no clue where to start or what to do!


radical 8ab^2 times (- radical 10a^3 b^4)

aorry i didnt know how to type them!!


Thanks for helping!

 

[pka]

If you do not want to use TeX why not read
http://www.karlscalculus.org/email.html?

 

[cvandoren]

i have but it still doesnt make any sense to me!!!!

 

[pka]

SORRY!
But we can only help those who will take the time to understand the notation.
If you refused to understand the symbols involves in the question, how can you expect to understand an answer.

 

[Gene]

You're going after the wrong side.
sqrt(45) = sqrt(9*5) = 3sqrt(5)

sqrt(8ab^2)*-sqrt(10a^3b^4) =
sqrt(80a^4b^5) =
sqrt((16a^4b^4)*(5b))

 

[soroban]

Hello, cvandoren!

$\displaystyle 8\sqrt{5}\,-\,2\sqrt{45}$

Heres what I got so far:

$\displaystyle 8\sqrt{5}$ can be reduced to $\displaystyle 2\sqrt{5}$ . . . really??

How did you change the "8" to a "2" ?

Evidently, you don't understand Simplifying Radicals.

The basic rule we use is: $\displaystyle \;\sqrt{a\cdot b}\:=\:\sqrt{a}\cdot\sqrt{b}$
. . The square root of a product may be "split" into two square roots.


Example: Simplify $\displaystyle \sqrt{45}$

Try to factor the 45 into two parts, where one part is a square number.

. . We find that $\displaystyle 45\:=\:5\,\times\,9$ . . . and 9 is a square.

So we have: $\displaystyle \;\sqrt{45}\;=\;\sqrt{9\cdot5}$ . . . I always put the square "in front"

. . Then we can "split" it: $\displaystyle \sqrt{9\cdot5}\;=\;\sqrt{9}\cdot\sqrt{5}$

We know that $\displaystyle \sqrt{9}\,=\,3$ ... and we're stuck with the $\displaystyle \sqrt{5}$.

. . So we have: $\displaystyle \;3\sqrt{5}$


Back to the original problem: $\displaystyle \;8\sqrt{5}\,-\,2\sqrt{45}$

We just learned that $\displaystyle \sqrt{45}\,=\,3\sqrt{5}$, right?

. . So we have: $\displaystyle \;8\sqrt{5}\,-\,2\cdot3\sqrt{5} \;= \;8\sqrt{5}\,-\,6\sqrt{5}$

Can we combine them? .Yes, it's exactly like $\displaystyle 8x\,-\,6x$ ("like" terms)

Answer: $\displaystyle \;2\sqrt{5}$