exponent and radical simplification

let the side of cube be x...ac=x

distance of bc=(3^0.5)x=1.732x

distance of ab=(2^0.5)x=1.414x

difference=1.732x-1.414x=0.318x~==0.3x

0.3x is 30% of x.....hope it clears

Thanks so much for your response

how did you arrive at bc=(3^0.5)x and ab=(2^0.5)x ???



distance of bc=(3^0.5)x=1.732x

distance of ab=(2^0.5)x=1.414x


Thanks

using pythagoras theorem..
u will b able to find line segment BC
and similarly AB
Let AC=x

Thus BC=root of( x^2 + x^2 ) + x^2 = x root3=1.732x
AB= root of( x^2 + x^2 ) = x root2=1.414x

Thus BC- AB = 0.318x

i.e 0.318x/ x * 100 = 30% (approx.)

I feel like an idiot. I understand pythag theorem. Maybe I am forgetting some rules about simplifying radicals and exponents? any suiggestions?

raunekk wrote:
Thus BC=root of( x^2 + x^2 ) + x^2 = x root3=1.732x
AB= root of( x^2 + x^2 ) = x root2=1.414x

I must have forgotten this rule of roots/exponents.

What is/are the rule/s for taking the square root of numbers with exponents?

I know that the general rule in simplifying the z'th root of (x^n) = x^n/z.
i.e. cubed root (x^2) = x^2/3.

How do you simplify when there is more than 1 term within a square root?

Lakers09 wrote:I feel like an idiot. I understand pythag theorem. Maybe I am forgetting some rules about simplifying radicals and exponents? any suiggestions?

If you are forgetting the basics on radical simplification then you should definitely check this link

https://math.tutorvista.com/number-syste ... icals.html