Melody

But it doesn't say "prove" Rosala, it is just a true statement.

If √0.09 * 0.9 * x = 0.9 * 0.09.√y , then find x/y

Do you mean that your teacher did not get sqrt y on the RHS.  That her answer was just a number?

Maybe this was your intended question.

$$\begin{array}{lr}
\\\sqrt{0.09 \times 0.9 \times x} = 0.9 \times 0.09\sqrt{y}\qquad then \;find \;\frac{x}{y}\qquad &\mbox{(1)} \\\\
square\; both\; sides &\mbox{(2)} \\\\
0.09\times 0.9\times x=0.9^2\times 0.09^2\times y &\mbox{(3)} \\\\
Divide\;both\;sides\;by\;0.09\times0.9 &\mbox{(4)} \\\\
x=0.9\times 0.09y &\mbox{(5)} \\\\
Divide\; both \;sides\; by \;y &\mbox{(6)} \\\\
\frac{x}{y}=0.9\times 0.09 &\mbox{(7)} \\\\
\frac{x}{y}=0.081 &\mbox{(8)}\\\\
\end{array}$$

Does that look better Rosala?  See if you can tell me what line you got lost at.  

And if you can tell me why.  The 1st line is just the question.  Make sure it is the question that you want. 

Anonymous, your exact method will only work if the coefficient of x² is 1.

When factorising always look for common factors first like Honga has done.

If there are no common factors - I mean when I cannot get the x² coefficient to equal 1 I use the  grouping method technique.

This video is good for factoring all types of quadratics.

There actually is no question here.

It is just a true statement.

6+(-4)= (-4)+6

But as Rosala has said the answer is 2.

Thanks Helen 

It is "asin"

Arcsine is the same as inverse sine.

Thanks Honga,

Do you understand Rosala?

Thanks Rosala.

We don't have teachers day in Australia.  I think it should be introduced.  

a+9-9=14-9

a=5

$$cube root of 125 = $\sqrt[3]{125}=125^{1/3}$$

on the calc this could be entered as  125^(1/3)