Simplify the expression
x times the square root of the quantity 64 x cubed, plus 2 x times the square root of x, plus 8 times the square root of the quantity 2 x

If the simplified expression is written in standard form, what is the leading coefficient?

Question

Simplify the expression
 x times the square root of the quantity 64 x cubed, plus 2 x times the square root of x, plus 8 times the square root of the quantity 2 x 

If the simplified expression is written in standard form, what is the leading coefficient?

mikezack123 · Answer

please help! medal will be given

mikezack123 · Answer

@e.mccormick @Hero @Luigi0210 @marissalovescats @mathmale @Preetha @whpalmer4

marissalovescats · Answer

Could you draw the problem so we can see it

marissalovescats · Answer

Remember that with adding radicals, you can only add similar radicals. So what is under the radical has to be the same number.

e.mccormick · Answer

x times the square root of the quantity 64 x cubed, plus 2 x times the square root of x, plus 8 times the square root of the quantity 2 x 
$x\sqrt{64x^3}+2x\sqrt{x}+8\sqrt{2x}$

e.mccormick · Answer

That, or what?

mikezack123 · Answer

yes that is how it looks @e.mccormick

mikezack123 · Answer

@marissalovescats

e.mccormick · Answer

So first, take anything out from under the radicals that you can.

mikezack123 · Answer

how? @e.mccormick i don't understand it at all... can you give steps pleaseeee

mikezack123 · Answer

@e.mccormick

e.mccormick · Answer

$\sqrt{48}=\sqrt{4\cdot4\cdot3}=4\sqrt{3}$

$\sqrt{a^5}=\sqrt{aa^2a^2}=a^2\sqrt{a}$

e.mccormick · Answer

That is the short explanation. The full version is here: http://www.purplemath.com/modules/radicals.htm But basically, anything that is squared can come out from under a square root. Anything that is cubed can come out from under a cube root.

mikezack123 · Answer

@e.mccormick would the leading coefficient be 8?

e.mccormick · Answer

For the first one, yes.  Do you see anything else you can get out of that root?

mikezack123 · Answer

umm....

mikezack123 · Answer

not really.... does that mean my answer is incomplete?

e.mccormick · Answer

$8x\sqrt{x^3}+2x\sqrt{x}+8\sqrt{2x}$

Well, $x^3=x\cdot x\cdot x $

mikezack123 · Answer

but its just asking for the leading so it would be 8 right? cuz its fill in the blank

e.mccormick · Answer

Well, it is asking two things.  The leading coefficent, in the present form, is unclear becaus it is not fully simplified.  You fully simplify first to be able to make sure of the rank.