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How do you simplify #root(3)(-54)#?

Answer 1

Benjamin Altschul

#root(3)(-54)=-3xxroot(3)2#

#root(3)(-54)#

#= root(3)((-3)xx(-3)xx(-3)xx2)#

#= -3xxroot(3)2#

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Answer 2

Skylar Adams

To simplify ( \sqrt[3]{-54} ), first factor out any perfect cubes from the radicand:

( -54 = -1 \times 2 \times 3^3 )

Then, extract the cube root of the perfect cube:

( \sqrt[3]{-54} = \sqrt[3]{-1 \times 2 \times 3^3} = \sqrt[3]{-1} \times \sqrt[3]{2} \times \sqrt[3]{3^3} = -1 \times \sqrt[3]{2} \times 3 = -3\sqrt[3]{2} )

So, ( \sqrt[3]{-54} ) simplifies to ( -3\sqrt[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.