2

Let's say I am to multiply $3x^2$ by ${\sqrt 8}$.
Which answer is true and why?

$3 {\sqrt 8x^2}$

or

$3x^2 {\sqrt 8}$

Jean Marie
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Steve
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    The two are mathematically the same, so they are technically both true. However, the first form is the one commonly used, since it groups the constants together $3 \sqrt{8}$ and separates the variable $x^2$ at the end. – dxiv Aug 27 '17 at 05:08
  • @dxiv how come is $x^2$ separated as it's multiplied with $8$ under the square root? – Steve Aug 27 '17 at 05:23
  • Where do you see $x^2$ under the square root? $;3\sqrt{8},x^2 = 3\sqrt{8} \cdot x^2 \ne 3 \sqrt{8 x^2},$. – dxiv Aug 27 '17 at 05:25
  • @dxiv Ah, I was so confused as I thought both $8$ and $x^2$ are under the square root. Thanks, now I get it) – Steve Aug 27 '17 at 05:29
  • I have seen the second form. I believe it's for clarity's sake. The idea being to clearly differentiate between $3\sqrt8x^2$ and $3\sqrt{8x^2}$. – Mike Aug 27 '17 at 05:52

1 Answers1

2

Are the same.

You can use the following laws.

For all reals $a$, $b$ and $c$ we have $$ab=ba$$ and $$(ab)c=a(bc).$$ Now, let $3=a$, $\sqrt8=b$ and $x^2=c$.

Thus, $$3\sqrt8x^2=abc=(ab)c=a(bc)=a(cb)=acb=3x^2\sqrt8$$

Michael Rozenberg
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  • What about this same scenario except 3 doesn't exist: multiplying $x^2$ by $\sqrt 8$. Can I write the product as $x^2\sqrt8$ or it must be written as $\sqrt 8x^2$ ? – Steve Aug 27 '17 at 10:57
  • @Steve They are the same again. You need to choose what is more comfortable for you. I like $x^2\sqrt8$, but I know that there are people which like $\sqrt8x^2$. – Michael Rozenberg Aug 27 '17 at 11:00