Question

3√(2x)=12. solve for x

Answer 1

Get the square root alone. So first divide that 3 out.
Then square and divide again.

Answer 2

what do you mean by that?

Answer 3

The goal is just to get "x" by itself.
\(3\sqrt{2x}=12\)
\((3\sqrt{12x})^2=12^2\) this will get rid of the square root
\(9(2x)=144\)
\(18x=144\)
\(x=\frac{144}{18}=8\)

Answer 4

oops on the second step I made a typo:
\((3\sqrt{2x})^2=12^2\)

Answer 5

thank you so much

Answer 6

That if you want it done for ya ;)

Answer 7

wait. @kirbykirby how did u get 9(2x)

Answer 8

Recall the rule \((a\cdot b)^2=a^2\cdot b^2\)

Here, you have \((3\sqrt{2x})^2\), so think of \(a=3\) and \(b=\sqrt{2x}\)
Thus, you get \((3\sqrt{2x})^2=3^2\cdot (\sqrt{2x})^2\)

Answer 9

yes but wouldn't the (√2x)^2 be √2x^2 ?

Answer 10

\(\sqrt{2x}\ne \sqrt{2}x\) do you see the difference?
You wrote √(2x) which I assumed you meant \(\sqrt{2x}\)

Answer 11

If you have trouble convincing yourself. Recall this:
\(\sqrt{x}\sqrt{y}=\sqrt{x y}\)
Thus, \((\sqrt{2x})^2=(\sqrt{2}\sqrt{x})^2=(\sqrt{2})^2(\sqrt{x})^2=2x\)

Answer 12

the third step is an application of the rule \((a\cdot b)^2=a^2\cdot b^2\) where \(a=\sqrt{2}\) and \(b=\sqrt{x}\)

Answer 13

but really, it's just easier to think of anything squared, under a square root, removed the square root. So even if you have a complicated expression under the square root, you can just remove it. For example:
\[\left(\sqrt{x+y^{1/2}+zx+\frac{2}{\pi}}\right)^2=x+y^{1/2}+zx+\frac{2}{\pi}\]

Answer 14

Hopefully I didn't scare you with that last expression ^ :)

Answer 15

lol its okay. thank u

Answer 16

i just figured it out. u simplified it

Answer 17

:)