KBB QR Answer Clarification

[predent777]

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d is the distance from vertex A to vertex B. What is the volume of the cube in terms of d?

The work in the answer solution is as follows:

Volume = (edge)^3
= x^3
= (d/sqrt 3)^3
= (d^3 / 3 sqrt 3) x (sqrt 3 / sqrt 3) <--- ???
= [d^3 (sqrt 3)] / 9


I get everything except where the sqrt 3 / sqrt 3 came from? I feel stupid but I would really appreciate why it has to be multiplied like that.

Thanks for the help. 🙂

 

[LuckMC11]

that sqrt3/sqrt3 comes in to get rid of the radical in the denominator. sqrt 3 times sqrt 3 is just 3, which is y there is a 9 in the denominator now (there was a 3 there, times 3 = 9). it is basically just multiplying it by a fancy "1". like how 2/2 is the same thing as 5/5, which is the same thing as sqrt 3/sqrt 3.

hope this helps!

 

[predent777]

that sqrt3/sqrt3 comes in to get rid of the radical in the denominator. sqrt 3 times sqrt 3 is just 3, which is y there is a 9 in the denominator now (there was a 3 there, times 3 = 9). it is basically just multiplying it by a fancy "1". like how 2/2 is the same thing as 5/5, which is the same thing as sqrt 3/sqrt 3.

hope this helps!

Totally overlooked simplifying answers. Got it now. Thank you. 🙂

 

[LuckMC11]

Totally overlooked simplifying answers. Got it now. Thank you. 🙂

no problem, dont oversimplify! i used to do that a few years ago and was getting stuff wrong when i know clearly what to do, after i changed my ways the world became a better place😀