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How do you simplify #root3(3/4)#?

Answer 1

Nathan Axel

#root(3)(3/4) = root(3)(6)/2#

For any non-zero values of #a, b# we have:

#root(3)(a/b) = root(3)(a)/root(3)(b)#

#root(3)(a^3) = a#

So we find:

#root(3)(3/4) = root(3)((3*2)/(4*2)) = root(3)(6/2^3) = root(3)(6)/root(3)(2^3) = root(3)(6)/2#

Notice how making the denominator into a perfect cube before splitting the radical allows us to avoid having to rationalise the denominator afterwards.

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Answer 2

Julia Adams

#color(blue)(root3(6)/2#

#root3(3/4)#

#:.=root3(3)/root3(4) xx root3(4)/root3(4) xx root3(4)/root3(4)#

#:.=color(blue)(root3(4)*root3(4)*root3(4)=4#

#:.=root3(48)/4#

#:.=root3(3*2*2*2*2)/4#

#:.=(cancel2^color(blue)1root3(6))/cancel4^color(blue)2#

#:.=color(blue)(root3(6)/2#

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Answer 3

Eva Abramson

To simplify √3(3/4), you can multiply the numbers inside and outside the square root. This gives you √(3 * 3/4). Simplifying further, you get √(9/4). Taking the square root of 9 gives you 3, and the square root of 4 gives you 2. Therefore, the simplified form of √3(3/4) is 3/2.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.