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How do you do the following math problems?
I have the answers, I just need to know how to show my work to get to the answer.
NO DECIMALS, all answers need to be done by hand.
Here are the problems--please go through each step:
8/cubed root of 2
5/cubed root of (5x)^2
2x/4 -- square root of 3
3/ square root of 5 + square root of 6
Sorry I don't have the symbols.
2 Answers
- XOMLv 41 decade agoFavorite Answer
1)
8/∛(2)
= 8/∛(2) x 1 x 1
=8/∛(2) x ∛(2)/∛(2) x ∛(2)/∛(2)
= [8 x ∛(2) x ∛(2) ]/2
= [4 x ∛(2) x ∛(2) ]
= 4∛(4)
__________________
2) Same as 1
5/∛(5x)^2
= 5/∛(25x^2)
= [5 * ∛(25x^2) * ∛(25x^2)]/(25x^2)
= ∛(25x^2)^2/(5x^2)
= ∛(625x^4)/(5x^2)
= (5x∛(5x))/(5x^2)
= ∛(5x))/x
_____________________
3)
2x/(4 -- √3)
= 2x/(4 + √3)
Multiply by conjugate
= 2x/(4 + √3) * (4 - √3) /(4 - √3)
= 2x(4 - √3) /(16 - 3)
= (x(8 - 2√3)) /13
_______________________
4)
3/(√5 + √6)
multiply by conjugate
= 3/(√5 + √6) * (√5 - √6)/(√5 - √6)
=3(√5 - √6)/(5 - 6)
=3(√5 - √6)/(-1)
= 3√6 - 3√5
______________________
- 1 decade ago
8 / [ 2 ^ (1/3) ] = [ 8 * (2^ (2/3)) ] / [ ( 2 ^ (1/3) ) * ( 2 ^ (2/3) ) ]
8 * 2^(2/3) / 2 = 4 * 2^(2/3)
multiply the denominator and numerator by whatever that causes it to get rid of the cube root.