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How do you evaluate #\root[ 3] { 2187} + 2\root [ 3] { 3}#?

Answer 1

Levi Adams

#root(3)2187+2root(3)3=11root(3)3#

#root(3)2187+2root(3)3#

= #root(3)(3xx3xx3xx3xx3xx3xx3)+2root(3)3#)

= #root(3)(ul(3xx3xx3)xxul(3xx3xx3)xx3)+2root(3)3#

= #3xx3xxroot(3)3+2root(3)3#

= #9root(3)3+2root(3)3#

= #11root(3)3#

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Answer 2

Emery Allen

To evaluate (\sqrt[3]{2187} + 2\sqrt[3]{3}), we first simplify the cube roots:

(\sqrt[3]{2187} = \sqrt[3]{3^7} = 3^{\frac{7}{3}} = 3^2 = 9)

(\sqrt[3]{3} = 3^{\frac{1}{3}})

Then, we substitute these values back into the expression:

(\sqrt[3]{2187} + 2\sqrt[3]{3} = 9 + 2(3^{\frac{1}{3}}))

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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.