how to work out 4*(sqrt(1+[9/16]*x^2)) ?

Question

how to work out 4*(sqrt(1+[9/16]*x^2))  ?

anonymous · Answer

$$4 * \sqrt{1 + \frac{ 9 }{ 16 }x2} $$

ivettef365 · Answer

do you have choices?

anonymous · Answer

i know the answer = $$\sqrt{(16+9x^2)}$$
just no idea the steps to take to achieve it

anonymous · Answer

write $4$ as $\sqrt{16}$ so you can multiply inside the radical

anonymous · Answer

$$4 \times  \sqrt{1 + \frac{ 9 }{ 16 }x2}=\sqrt{16}\times  \sqrt{1 + \frac{ 9 }{ 16 }x2}$$
$$=\sqrt{16(1+\frac{9}{16}x^2)}$$ etc

anonymous · Answer

oh thank you very much! just when I think im on top of uni calculus, I get stumped on something that was probably taught in grade 2...   thank you!

anonymous · Answer

yw
i have to add i see no reason why one form is any nicer than the other, i.e. why you would want to turn 
$$4  \sqrt{1 + \frac{ 9 }{ 16 }x^2}$$ into $$\sqrt{16+9x^2}$$ or vice versa

anonymous · Answer

in my case it stems from finding the derivative of sinh^-1 [3x/4]

anonymous · Answer

and the multiple choice answer to the quiz was in the format of the latter and so I had to confirm that I could simplify to that form in someway before I could know I had the right answer :)