Multiplying and Simplifying by Factoring

[PatriciaMann]

Multiply and Simplify
the square root of 8 times the square root of 40

 

[Deleted member 4993]

Multiply and Simplify
the square root of 8 times the square root of 40

\(\displaystyle \sqrt{8} * \sqrt{32} \ = \ \sqrt{8*32}\)

Now continue....

Please share your work with us, indicating exactly where you are stuck - so that we may know where to begin to help you.

 

[JeffM]

Multiply and Simplify
the square root of 8 times the square root of 40

\(\displaystyle \sqrt{8} * \sqrt{32} \ = \ \sqrt{8*32}\)

Now continue....

Please share your work with us, indicating exactly where you are stuck - so that we may know where to begin to help you.

Subhotosh Khan gave you an example. Let's generalize that example to ANY positive numbers.

Let a = the square root of b.
(1) Then a * a = b. That is a definition.

So let c = the square root of d.
(2) So c * c = d, again by definition.

(3) Let e = (b * d).
(4) Let f = the square root of e.
So, f * f = e, by definition.
So f * f = b * d by line 3.
So f * f = (a * a) * d by line 1.
So f * f = (a * a) * (c * c) by line 2.
So f * f = (a * c) * (a * c).
So f = (a * c).
So, if e = b * d, the square root of e = the square root of b TIMES the square root of d by lines 4, 1, and 2.

Subhotosh Khan's example is true for any pair of positive numbers.

So you should be able to do the first part of your problem quite easily now.

As for the second part that takes a little bit of insight.

Simplify \(\displaystyle \sqrt{405}\)
You need to factor 405, starting with prime factors and looking for a perfect square (if any).
Now 5 is obviously a prime factor.
So 405 = 5 * 81.
And 81 is a perfect square because 9 * 9 = 81.
So, \(\displaystyle \sqrt{405} = \sqrt{5*81} = \sqrt{81} * \sqrt{5} = 9\sqrt{5}\)
Edits in red. Thanks lookagain

 

[lookagain]

Post Deleted

Post Deleted

 

[mmm4444bot]

I deleted my post because I misread Subhotosh's example above as being the original exercise.

 

[Denis]

Multiply and Simplify
the square root of 8 times the square root of 40

Boy, poor Patricia asked a simple question!
This thread, by now, has probably scared the poor student away!!

RULE: sqrt(a) * sqrt(b) = sqrt(a*b)
sqrt(8) * sqrt(40) = sqrt(8 * 40) = sqrt(320)

Note that 64 * 5 = 320, and sqrt(64) = 8 ; so:
sqrt(320) = sqrt(64 * 5) = 8*sqrt(5)

Note: "How" to get 64 * 5 is something you'll probably be taught next.

 

[mmm4444bot]

sqrt(8) * sqrt(40) = sqrt(8 * 40) = sqrt(320)

Note that 64 * 5 = 320

sqrt(320) = sqrt(64 * 5) = 8*sqrt(5)

How 'bout this factoring:

sqrt(8) * sqrt(40) = sqrt(8) * sqrt(8*5) = sqrt(8^2*5) = 8sqrt(5)

Does not require knowing 320 = 5*64

 

[Denis]

Re:

sqrt(8) * sqrt(40) = sqrt(8 * 40) = sqrt(320)
Note that 64 * 5 = 320
sqrt(320) = sqrt(64 * 5) = 8*sqrt(5)

How 'bout this factoring:
sqrt(8) * sqrt(40) = sqrt(8) * sqrt(8*5) = sqrt(8^2*5) = 8sqrt(5)
Does not require knowing 320 = 5*64

AGREE 100% Mark.
However, I'm trying to make this point:
from the question by the student, we can see that she's in the learning stages;
so all she'll understand (at first) is what she's been taught;
for us to post stuff that's way beyond what she's been exposed to is a loss of time.
Like, if someone asks how to ride a tricycle, no need to mention anything about flying a plane!
I respect everybody's opinions here, but if not same as mine, than they're wrong

Subhotosh, have another look at your post...then head for the corner...

 

[JeffM]

Re: Re:

for us to post stuff that's way beyond what she's been exposed to is a loss of time. I do not think that anyone tried to go beyond what was requested of the student. She was asked to multiply and simplify and so there were two parts to her question. As to explaining the formula, I suspect that competence using it is improved by understanding it as well as memorizing it.

I respect everybody's opinions here, but if not same as mine, than they're wrong You have taken the words right out of my mouth. I respect your opinion, but, not being mine, it is wrong.

Subhotosh, have another look at your post...then head for the corner... Je pense que c'est vous, mon ami, qui faut aller au coin. Subhotosh a donne un example. Pardon my French; I may need to go to the language corner. Le coin, la coin? Are "coin" and "faut" even the right words? Un example, une example? Once in France, I explained that I did not want to tirer le voiture a nuit when I meant that I did not want to conduire le voiture a nuit. People thought that my nocturnal aversions were provincial and looked at me quite oddly.[/quote]

 

[Denis]

Let's leave it at this Jeff: your "written" French is better than mine;
I can only speak it fluently...but schooling was in English.

 

[lookagain]

Re:

How 'bout this factoring:

sqrt(8) * sqrt(40) = sqrt(8) * sqrt(8*5) = sqrt(8^2*5) = 8sqrt(5)

Does not require knowing 320 = 5*64

\(\displaystyle Or,\)

\(\displaystyle (\sqrt{8})\sqrt{40} \ = \\)

\(\displaystyle (\sqrt{8})\bigg[\sqrt{(8)(5)}\bigg] \ =\)

\(\displaystyle (\sqrt{8})(\sqrt{8})(\sqrt{5}) \ =\)

\(\displaystyle 8\sqrt{5}\)


---------------------------------------------------


\(\displaystyle \text{Here's another example:}\)


\(\displaystyle (\sqrt{8})(\sqrt{40})(\sqrt{55})(\sqrt{33}) \ = \\)

\(\displaystyle (\sqrt{8})\bigg[\sqrt{(8)(5)}\bigg]\bigg[\sqrt{(5)(11)}\bigg]\bigg[\sqrt{(11)(3)}\bigg] \ =\)

\(\displaystyle (\sqrt{8})(\sqrt{8})(\sqrt{5})(\sqrt{5})(\sqrt{11})(\sqrt{11})(\sqrt{3}) \ =\)

\(\displaystyle (8)(5)(11)\sqrt{3} \ =\)

\(\displaystyle \boxed{440\sqrt{3}}\)

 

[Deleted member 4993]

Re: Re:

Subhotosh, have another look at your post...then head for the corner... Subhotosh a donne un example.

Ha..ha..ha - I have supporter now - you go to corner for misunderstanding my deed .....

 

[Denis]

Oh no you don't: I do not see an introductory "as example"...