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Mathematics 8 Online
OpenStudy (anonymous):

Plz help fast Simplify √8•6√5=

OpenStudy (anonymous):

use a calculator

OpenStudy (anonymous):

no find the square root of 8 then multiply by 6 then multiply by the square root of 5

OpenStudy (whpalmer4):

\[\sqrt{8}*6*\sqrt{5} = 6*\sqrt{8}*\sqrt{5} = 6*\sqrt{8*5} = 6*\sqrt{40}\]\[ = 6*\sqrt{4*10} = 6*\sqrt{4}*\sqrt{10} = 6*2*\sqrt{10} = \]

OpenStudy (anonymous):

wolframalpha.com agrees with my answer

OpenStudy (whpalmer4):

The problem asks to simplify, not find the decimal...

OpenStudy (anonymous):

oh very true

OpenStudy (whpalmer4):

as both \(\sqrt{8}\) and \(\sqrt{5}\) are irrational, it is not possible to multiply them accurately except by doing so symbolically, which is what we did.

OpenStudy (whpalmer4):

I should say exactly, not accurately...

OpenStudy (anonymous):

So what's my answer going to be please

OpenStudy (whpalmer4):

\(6*2*\sqrt{10} = \) ? what is \(6*2=\) what do you get if you multiply that by \(\sqrt{10}\) hint: \(a * \sqrt{b} = a\sqrt{b}\)

OpenStudy (anonymous):

2^2=2

OpenStudy (anonymous):

I really don't know

OpenStudy (whpalmer4):

You don't know what \(6*2=\) seriously?

OpenStudy (anonymous):

12

OpenStudy (whpalmer4):

okay, and a number times a square root of a number is written number square root other number. \[2*\sqrt{3} = 2\sqrt{3}\] \[12 * \sqrt{10} = \]

OpenStudy (anonymous):

I Don't know

OpenStudy (anonymous):

Is it the finale answer √120

OpenStudy (whpalmer4):

I can't make it any plainer than I just did...if you multiply a number by the square root of another number, you just write down the first number followed by the square root sign and the other number, just like I did for 2 * the square root of 3.

OpenStudy (whpalmer4):

No, if you move a number from the inside of the square root to the outside, you have to take the square root of the number. \[\sqrt{32} = \sqrt{16*2} = \sqrt{16}*\sqrt{2} = 4*\sqrt{2} = 4\sqrt{2}\] Going the other way, if you move a number inside the square root sign, you have to square it: \[10\sqrt{2} = \sqrt{10*10}*\sqrt{2} = \sqrt{10*10*2} = \sqrt{200}\] So, if you wanted to move that \(12\) inside the square root sign, it would be: \[12\sqrt{10} = \sqrt{12*12}*\sqrt{10}=\sqrt{12*12*10}= \sqrt{1440}\]

OpenStudy (whpalmer4):

Your answer is simply \(12\sqrt{10}\) — that is the simplified form of \(\sqrt{8}*6*\sqrt{5}\)

OpenStudy (anonymous):

Ohh ok thank you

OpenStudy (whpalmer4):

I suggest you ask your teacher to go over this with you again, as it is very important, and you'll have no end of trouble if you make mistakes...

OpenStudy (anonymous):

Ok thanks I am homeschool

OpenStudy (whpalmer4):

Hmm. Have you tried watching the Khan Academy ( http://khanacademy.org) videos? They are generally very good, I find. Here's the section on square roots: https://www.khanacademy.org/math/pre-algebra/exponents-radicals/radical-radicals/v/understanding-square-roots I think you would probably be well-served to go through the whole pre-algebra lecture series. Not all in one afternoon, of course! :-)

OpenStudy (anonymous):

Thanks

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